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Journal articles on the topic 'Ising'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2025

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1

Pan, Zhenyu, Anshujit Sharma, Jerry Yao-Chieh Hu, Zhuo Liu, Ang Li, Han Liu, Michael Huang, and Tony Geng. "Ising-Traffic: Using Ising Machine Learning to Predict Traffic Congestion under Uncertainty." Proceedings of the AAAI Conference on Artificial Intelligence 37, no. 8 (June 26, 2023): 9354–63. http://dx.doi.org/10.1609/aaai.v37i8.26121.

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This paper addresses the challenges in accurate and real-time traffic congestion prediction under uncertainty by proposing Ising-Traffic, a dual-model Ising-based traffic prediction framework that delivers higher accuracy and lower latency than SOTA solutions. While traditional solutions face the dilemma from the trade-off between algorithm complexity and computational efficiency, our Ising-based method breaks away from the trade-off leveraging the Ising model's strong expressivity and the Ising machine's strong computation power. In particular, Ising-Traffic formulates traffic prediction under uncertainty into two Ising models: Reconstruct-Ising and Predict-Ising. Reconstruct-Ising is mapped onto modern Ising machines and handles uncertainty in traffic accurately with negligible latency and energy consumption, while Predict-Ising is mapped onto traditional processors and predicts future congestion precisely with only at most 1.8% computational demands of existing solutions. Our evaluation shows Ising-Traffic delivers on average 98X speedups and 5% accuracy improvement over SOTA.

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2

Gębura, Andrzej, Kazimierz Janusiak, and Michał Poradowski. "An Icing Of Aircraft – Reasons, Consequences, Counteraction." Journal of KONBiN 32, no. 1 (December 1, 2014): 57–70. http://dx.doi.org/10.2478/jok-2014-0031.

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Abstract The article presents reasons of an helicopter’s ising as well as an aircraft’s ising. The maion attention is addressed a conteraction of an ising. Autors divide the problem an two groups: an ising of an airframe – mostly lifting surfaces, an ising of engines. According to authors reasons, an extension (first of all) consequences of airframe’s ising considerably differ from seemingly similar events in an engine. The considerable attention is concentrated on a connteraction of consequences of an ising during the flight. The most complicated ising referes to helicopters, considering their particular aerodynamics characteristics. The autors dedicated is greather attention. Results reached during investigations of heating rotor blades in ITWL are presented.

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3

Chen, Wenhan, Haodi Tang, Yu Wang, Xianwu Hu, Yuming Lin, Tai Min, and Yufeng Xie. "E-Spin: A Stochastic Ising Spin Based on Electrically-Controlled MTJ for Constructing Large-Scale Ising Annealing Systems." Micromachines 14, no. 2 (January 19, 2023): 258. http://dx.doi.org/10.3390/mi14020258.

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With its unique computer paradigm, the Ising annealing machine has become an emerging research direction. The Ising annealing system is highly effective at addressing combinatorial optimization (CO) problems that are difficult for conventional computers to tackle. However, Ising spins, which comprise the Ising system, are difficult to implement in high-performance physical circuits. We propose a novel type of Ising spin based on an electrically-controlled magnetic tunnel junction (MTJ). Electrical operation imparts true randomness, great stability, precise control, compact size, and easy integration to the MTJ-based spin. In addition, simulations demonstrate that the frequency of electrically-controlled stochastic Ising spin (E-spin) is 50 times that of the thermal disturbance MTJ-based spin (p-bit). To develop a large-scale Ising annealing system, up to 64 E-spins are implemented. Our Ising annealing system demonstrates factorization of integers up to 264 with a temporal complexity of around O(n). The proposed E-spin shows superiority in constructing large-scale Ising annealing systems and solving CO problems.

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4

Horiguchi, Tsuyoshi, Adam Lipowski, and Norihiro Tsushima. "ising model and two-layer Ising model." Physica A: Statistical Mechanics and its Applications 224, no. 3-4 (February 1996): 626–38. http://dx.doi.org/10.1016/0378-4371(95)00304-5.

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5

Barry, J. H., and M. Khatun. "Exact Solutions for Correlations in the Kagomé Ising Antiferromagnet." International Journal of Modern Physics B 11, no. 01n02 (January 20, 1997): 93–101. http://dx.doi.org/10.1142/s0217979297000113.

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The kagomé Ising antiferromagnet is highly frustrated with its pair correlation decaying exponentially at large distance for all temperatures including absolute zero. Hence, the spin system does not support long-range orderings and is devoid of any phase transition. One proves, via local star-triangle and decoration-decimation transformations, that correlations in the kagomé Ising antiferromagnet at arbitrary temperatures can be represented as linear combinations of correlations in the honeycomb Ising ferromagnet at high temperatures (disordered region). Existent knowledge of all honeycomb Ising correlations upon a select (spatially compact) 10-site cluster is thus sufficient to determine all present kagomé Ising correlations upon an associated 9-site cluster. Examples of resulting exact solutions for pair and multisite correlations in the kagomé Ising antiferromagnet are presented at all temperatures. Applications include joint configuration probabilities, thermodynamic response functions such as the specific heat and the initial perpendicular susceptibility, and the inelastic neutron scattering function.

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6

Nareddy, Vahini Reddy, Jonathan Machta, Karen C. Abbott, Shadisadat Esmaeili, and Alan Hastings. "Dynamical Ising model of spatially coupled ecological oscillators." Journal of The Royal Society Interface 17, no. 171 (October 2020): 20200571. http://dx.doi.org/10.1098/rsif.2020.0571.

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Long-range synchrony from short-range interactions is a familiar pattern in biological and physical systems, many of which share a common set of ‘universal’ properties at the point of synchronization. Common biological systems of coupled oscillators have been shown to be members of the Ising universality class, meaning that the very simple Ising model replicates certain spatial statistics of these systems at stationarity. This observation is useful because it reveals which aspects of spatial pattern arise independently of the details governing local dynamics, resulting in both deeper understanding of and a simpler baseline model for biological synchrony. However, in many situations a system’s dynamics are of greater interest than their static spatial properties. Here, we ask whether a dynamical Ising model can replicate universal and non-universal features of ecological systems, using noisy coupled metapopulation models with two-cycle dynamics as a case study. The standard Ising model makes unrealistic dynamical predictions, but the Ising model with memory corrects this by using an additional parameter to reflect the tendency for local dynamics to maintain their phase of oscillation. By fitting the two parameters of the Ising model with memory to simulated ecological dynamics, we assess the correspondence between the Ising and ecological models in several of their features (location of the critical boundary in parameter space between synchronous and asynchronous dynamics, probability of local phase changes and ability to predict future dynamics). We find that the Ising model with memory is reasonably good at representing these properties of ecological metapopulations. The correspondence between these models creates the potential for the simple and well-known Ising class of models to become a valuable tool for understanding complex biological systems.

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7

Angst, Sebastian, Silvio R. Dahmen, Haye Hinrichsen, Alfred Hucht, and Martin P. Magiera. "Explosive Ising." Journal of Statistical Mechanics: Theory and Experiment 2012, no. 06 (June 27, 2012): L06002. http://dx.doi.org/10.1088/1742-5468/2012/06/l06002.

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8

Nisoli, Cristiano. "Nano-Ising." New Journal of Physics 18, no. 2 (February 24, 2016): 021007. http://dx.doi.org/10.1088/1367-2630/18/2/021007.

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9

Stajic, Jelena. "Ising Ice." Science 338, no. 6103 (October 4, 2012): 17.2–17. http://dx.doi.org/10.1126/science.338.6103.17-b.

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10

Huang, Ding-wei. "Ising intermittency." European Physical Journal C 5, no. 3 (1998): 567. http://dx.doi.org/10.1007/s100520050301.

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11

Huang, Ding-wei. "Ising intermittency." European Physical Journal C 5, no. 3 (September 1998): 567–74. http://dx.doi.org/10.1007/s100529800870.

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12

Stutz, Conley, and Beverly Williams. "Ernst Ising." Physics Today 52, no. 3 (March 1999): 106–8. http://dx.doi.org/10.1063/1.882538.

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13

Mondal, Ankit, and Ankur Srivastava. "Ising-FPGA." ACM Transactions on Design Automation of Electronic Systems 26, no. 1 (January 5, 2021): 1–27. http://dx.doi.org/10.1145/3411511.

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14

Yan, Mu-lin. "Ising-Gauge Ising-Higgs System in Two Dimensions." Communications in Theoretical Physics 4, no. 5 (September 1985): 757–58. http://dx.doi.org/10.1088/0253-6102/4/5/757.

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15

Johnston, Desmond A., and Ranasinghe P. K. C. M. Ranasinghe. "(Four) Dual Plaquette 3D Ising Models." Entropy 22, no. 6 (June 8, 2020): 633. http://dx.doi.org/10.3390/e22060633.

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A characteristic feature of the 3 d plaquette Ising model is its planar subsystem symmetry. The quantum version of this model has been shown to be related via a duality to the X-Cube model, which has been paradigmatic in the new and rapidly developing field of fractons. The relation between the 3 d plaquette Ising and the X-Cube model is similar to that between the 2 d quantum transverse spin Ising model and the Toric Code. Gauging the global symmetry in the case of the 2 d Ising model and considering the gauge invariant sector of the high temperature phase leads to the Toric Code, whereas gauging the subsystem symmetry of the 3 d quantum transverse spin plaquette Ising model leads to the X-Cube model. A non-standard dual formulation of the 3 d plaquette Ising model which utilises three flavours of spins has recently been discussed in the context of dualising the fracton-free sector of the X-Cube model. In this paper we investigate the classical spin version of this non-standard dual Hamiltonian and discuss its properties in relation to the more familiar Ashkin–Teller-like dual and further related dual formulations involving both link and vertex spins and non-Ising spins.

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16

Akın, Hasan. "Calculation of the Free Energy of the Ising Model on a Cayley Tree via the Self-Similarity Method." Axioms 11, no. 12 (December 7, 2022): 703. http://dx.doi.org/10.3390/axioms11120703.

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In this study, an interactive Ising model having the nearest and prolonged next-nearest neighbors defined on a Cayley tree is considered. Inspired by the results obtained for the one-dimensional Ising model, we will construct the partition function and then calculate the free energy of the Ising model having the prolonged next nearest and nearest neighbor interactions and external field on a two-order Cayley tree using the self-similarity of the semi-infinite Cayley tree. The phase transition problem for the Ising system is investigated under the given conditions.

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17

MARKO, P., M. KUPKA, and P. KOPČANSKÝ. "THE ANNEALED MANY-BONDS ISING MODEL." Modern Physics Letters B 05, no. 06 (March 10, 1991): 465–70. http://dx.doi.org/10.1142/s021798499100054x.

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The random bond problem with many kinds of bonds for Ising lattice is studied. The transformation was found from the Ising model with many kinds of bonds to the Ising problem with one effective bond. The method of transformation is illustrated on the 2D square lattice with ferromagnetic and antiferromagnetic interactions.

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18

Reungyos, Jutarop, and Yongyut Laosiritaworn. "Random Walk Monte Carlo Simulation of Diffusive Ferromagnetic Ising Spin under Lennard-Jones Interaction." Applied Mechanics and Materials 431 (October 2013): 57–60. http://dx.doi.org/10.4028/www.scientific.net/amm.431.57.

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This work investigated properties of diffusive magnetic particles. Random walk Monte Carlo method was used to simulate the Ising spin diffusing and flipping to examine the properties of the system. The Ising spins interact among themselves via Lennard-Jones interaction. Metropolis algorithm was employed to update spins configuration on the continuous space. The volume of Ising spins, magnetization and magnetic susceptibility, were investigated as functions of temperature, number of Ising spins in the system and simulation time. It was found that, at low temperatures, the Ising spins tend to stay close even at long simulation time, where finite magnetization was found suggesting the ferromagnetic preference. However, at high temperatures, paramagnetic behavior reveals as ferromagnetic interaction ceases with time passing. This is due to role of spin diffusing which causes the spins to disperse and hence ferromagnetic interaction among spins reduces.

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19

Hamerly, Ryan, Kensuke Inaba, Takahiro Inagaki, Hiroki Takesue, Yoshihisa Yamamoto, and Hideo Mabuchi. "Topological defect formation in 1D and 2D spin chains realized by network of optical parametric oscillators." International Journal of Modern Physics B 30, no. 25 (September 28, 2016): 1630014. http://dx.doi.org/10.1142/s0217979216300140.

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A network of optical parametric oscillators (OPOs) is used to simulate classical Ising and XY spin chains. The collective nonlinear dynamics of this network, driven by quantum noise rather than thermal fluctuations, seeks out the Ising/XY ground state as the system transitions from below to above the lasing threshold. We study the behavior of this “Ising machine” for three canonical problems: a 1D ferromagnetic spin chain, a 2D square lattice and problems where next-nearest-neighbor couplings give rise to frustration. If the pump turn-on time is finite, topological defects form (domain walls for the Ising model, winding number and vortices for XY) and their density can be predicted from a numerical model involving a linear “growth stage” and a nonlinear “saturation stage”. These predictions are compared against recent data for a 10,000-spin 1D Ising machine.

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20

Elidrysy, A., S. Harir, A. Zouhair, and Y. Boughaleb. "Anisotropic Effect on Local Magnetic Properties of 3D Extended Ising Model." SPIN 10, no. 03 (August 14, 2020): 2050015. http://dx.doi.org/10.1142/s2010324720500150.

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The magnetic properties of anisotropic 3D Ising model on a cubic lattice are studied by Monte Carlo simulation. In particular, we have considered an extended 3D Ising model with spatially uniaxial anisotropic bond randomness on the simple cubic lattice parameterized by exchange interaction parameter [Formula: see text], anisotropy parameter [Formula: see text] and external longitudinal magnetic field [Formula: see text]. The obtained numerical data clearly point out a second-order ferromagnetic-paramagnetic phase transition belonging in the same universality class with the 3D random Ising model at critical temperature [Formula: see text] that is strongly correlated to [Formula: see text] and [Formula: see text]. Especially, in the limit, [Formula: see text], the spin ½ cubic lattice becomes a collection of noncorrelated Ising chains, whereas in the other limit, [Formula: see text], the system becomes a stack of noncorrelated Ising square lattice.

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21

CHOI, Y. S., J. MACHTA, P. TAMAYO, and L. X. CHAYES. "PARALLEL INVADED CLUSTER ALGORITHM FOR THE ISING MODEL." International Journal of Modern Physics C 10, no. 01 (February 1999): 1–16. http://dx.doi.org/10.1142/s0129183199000024.

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A parallel version of the invaded cluster algorithm is described. Results from large scale (up to 40962 and 5123) simulations of the Ising model are reported. No evidence of critical slowing down is found for the three-dimensional Ising model. The magnetic exponent is estimated to be 2.482±0.001(β/ν=0.518±0.001) for the three-dimensional Ising model.

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22

Zhang, Zhidong, and Osamu Suzuki. "A Method of the Riemann–Hilbert Problem for Zhang’s Conjecture 2 in a Ferromagnetic 3D Ising Model: Topological Phases." Mathematics 9, no. 22 (November 18, 2021): 2936. http://dx.doi.org/10.3390/math9222936.

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A method of the Riemann–Hilbert problem is employed for Zhang’s conjecture 2 proposed in Philo. Mag. 87 (2007) 5309 for a ferromagnetic three-dimensional (3D) Ising model in a zero external magnetic field. In this work, we first prove that the 3D Ising model in the zero external magnetic field can be mapped to either a (3 + 1)-dimensional ((3 + 1)D) Ising spin lattice or a trivialized topological structure in the (3 + 1)D or four-dimensional (4D) space (Theorem 1). Following the procedures of realizing the representation of knots on the Riemann surface and formulating the Riemann–Hilbert problem in our preceding paper [O. Suzuki and Z.D. Zhang, Mathematics 9 (2021) 776], we introduce vertex operators of knot types and a flat vector bundle for the ferromagnetic 3D Ising model (Theorems 2 and 3). By applying the monoidal transforms to trivialize the knots/links in a 4D Riemann manifold and obtain new trivial knots, we proceed to renormalize the ferromagnetic 3D Ising model in the zero external magnetic field by use of the derivation of Gauss–Bonnet–Chern formula (Theorem 4). The ferromagnetic 3D Ising model with nontrivial topological structures can be realized as a trivial model on a nontrivial topological manifold. The topological phases generalized on wavevectors are determined by the Gauss–Bonnet–Chern formula, in consideration of the mathematical structure of the 3D Ising model. Hence we prove the Zhang’s conjecture 2 (main theorem). Finally, we utilize the ferromagnetic 3D Ising model as a platform for describing a sensible interplay between the physical properties of many-body interacting systems, algebra, topology, and geometry.

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23

WU, HAINA, ZHIHUA YANG, JIANHUI DAI, and HEPING YING. "RIGOROUS RESULTS FOR THE QUANTUM PHASE TRANSITIONS IN A DIMERIZED S = 1 ISING LATTICE." Modern Physics Letters A 22, no. 07n10 (March 28, 2007): 727–31. http://dx.doi.org/10.1142/s0217732307023328.

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We examine the ground state properties of a dimerized ferromagnetic S = 1 Ising chain with single-ion crystal fields by mapping the model onto the dimerized S = 1/2 Ising chain with transverse fields. We show that the system exhibits a series of Ising transitions depending on the dimerization strength of the crystal fields, while the critical points can be determined exactly.

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24

Ren, Qing-Bao, Meng-Bo Luo, and Qing-Hu Chen. "Transport Properties of the f=1/2 Square Lattice Coulomb Gas Model at the Ising-Like Phase Transition Temperature." International Journal of Modern Physics B 17, no. 22n24 (September 30, 2003): 4327–31. http://dx.doi.org/10.1142/s0217979203022398.

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The transport properties of the f=1/2 square lattice Coulomb gas model at the Ising-like phase transition temperature are studied using Monte Carlo technique. A non-Ohmic transport property is found at the Ising-like phase transition temperature Tc, indicating that the Ising-like phase transition is influenced by the KT phase transition and some vortices are bound neutrally at Tc.

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25

Kumagai, Masahito, Kazuhiko Komatsu, Masayuki Sato, and Hiroaki Kobayashi. "Ising-Based Kernel Clustering." Algorithms 16, no. 4 (April 19, 2023): 214. http://dx.doi.org/10.3390/a16040214.

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Combinatorial clustering based on the Ising model is drawing attention as a high-quality clustering method. However, conventional Ising-based clustering methods using the Euclidean distance cannot handle irregular data. To overcome this problem, this paper proposes an Ising-based kernel clustering method. The kernel clustering method is designed based on two critical ideas. One is to perform clustering of irregular data by mapping the data onto a high-dimensional feature space by using a kernel trick. The other is the utilization of matrix–matrix calculations in the numerical libraries to accelerate preprocess for annealing. While the conventional Ising-based clustering is not designed to accept the transformed data by the kernel trick, this paper extends the availability of Ising-based clustering to process a distance matrix defined in high-dimensional data space. The proposed method can handle the Gram matrix determined by the kernel method as a high-dimensional distance matrix to handle irregular data. By comparing the proposed Ising-based kernel clustering method with the conventional Euclidean distance-based combinatorial clustering, it is clarified that the quality of the clustering results of the proposed method for irregular data is significantly better than that of the conventional method. Furthermore, the preprocess for annealing by the proposed method using numerical libraries is by a factor of up to 12.4 million × from the conventional naive python’s implementation. Comparisons between Ising-based kernel clustering and kernel K-means reveal that the proposed method has the potential to obtain higher-quality clustering results than the kernel K-means as a representative of the state-of-the-art kernel clustering methods.

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26

Ferrari, Patrik L., and Senya Shlosman. "The Airy₂ process and the 3D Ising model." Journal of Physics A: Mathematical and Theoretical 56, no. 1 (January 6, 2023): 014003. http://dx.doi.org/10.1088/1751-8121/acb247.

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Abstract The Ferrari–Spohn diffusion process arises as limit process for the 2D Ising model as well as random walks with area penalty. Motivated by the 3D Ising model, we consider M such diffusions conditioned not to intersect. We show that the top process converges to the Airy2 process as M → ∞ . We then explain the relation with the 3D Ising model and present some conjectures about it.

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27

Zhang, Yi, Yi Deng, Yinan Lin, Yang Jiang, Yujiao Dong, Xi Chen, Guangyi Wang, et al. "Oscillator-Network-Based Ising Machine." Micromachines 13, no. 7 (June 27, 2022): 1016. http://dx.doi.org/10.3390/mi13071016.

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With the slowdown of Moore’s law, many emerging electronic devices and computing architectures have been proposed to sustain the performance advancement of computing. Among them, the Ising machine is a non-von-Neumann solver that has received wide attention in recent years. It is capable of solving intractable combinatorial optimization (CO) problems, which are difficult to be solve using conventional digital computers. In fact, many CO problems can be mapped to finding the corresponding ground states of Ising model. At present, Ising machine prototypes based on different physical principles, such as emerging memristive oscillators, have been demonstrated, among which the Ising Hamiltonian solver based on the coupled oscillator network simultaneously holds the advantages of room-temperature operation, compact footprint, low power consumption, and fast speed to solution. This paper comprehensively surveys the recent developments in this important field, including the types of oscillators, the implementation principle of the Ising model, and the solver’s performance. Finally, methods to further improve the performance have also been suggested.

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28

Ito, N., M. Taiji, and M. Suzuki. "CRITICAL DYNAMICS OF THE ISING MODEL WITH ISING MACHINE." Le Journal de Physique Colloques 49, no. C8 (December 1988): C8–1397—C8–1398. http://dx.doi.org/10.1051/jphyscol:19888641.

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29

Horiguchi, Tsuyoshi. "Decomposition of Ising spin of spin-S Ising model." Physica A: Statistical Mechanics and its Applications 214, no. 3 (March 1995): 452–60. http://dx.doi.org/10.1016/0378-4371(94)00283-y.

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30

Magare, Sourabh, Abhinash Kumar Roy, and Varun Srivastava. "1D Ising model using the Kronecker sum and Kronecker product." European Journal of Physics 43, no. 3 (March 21, 2022): 035102. http://dx.doi.org/10.1088/1361-6404/ac5637.

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Abstract Calculations in the Ising model can be cumbersome and non-intuitive. Here we provide a formulation that addresses these issues for 1D scenarios. We represent the microstates of spin interactions as a diagonal matrix. This is done using two operations: the Kronecker sum and Kronecker product. The calculations thus become a simple matter of manipulating diagonal matrices. We address the following problems in this work: spins in the magnetic field, open-chain 1D Ising model, closed-chain 1D Ising model and the 1D Ising model in an external magnetic field. We believe that this representation will help provide students and experts with a simple yet powerful technique to carry out calculations in this model.

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31

LIMA, F. W. S. "TAX EVASION AND NONEQUILIBRIUM MODEL ON APOLLONIAN NETWORKS." International Journal of Modern Physics C 23, no. 11 (November 2012): 1250079. http://dx.doi.org/10.1142/s0129183112500799.

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The Zaklan model had been proposed and studied recently using the equilibrium Ising model on square lattices (SLs) by [G. Zaklan, F. Westerhoff and D. Stauffer, J. Econ. Interact. Coord.4, 1 (2008), arXiv:0801.2980; G. Zaklan, F. W. S. Lima and F. Westerhoff, Physica A387, 5857 (2008)], near the critical temperature of the Ising model presenting a well-defined phase transition; but on normal and modified Apollonian networks (ANs), [J. S. Andrade, Jr., H. J. Herrmann, R. F. S. Andrade, and L. R. da Silva, Phys. Rev. Lett.94, 018702 (2005); R. F. S. Andrade, J. S. Andrade Jr. and H. J. Herrmann, Phys. Rev. E79, 036105 (2009)] studied the equilibrium Ising model. They showed the equilibrium Ising model not to present on ANs a phase transition of the type for the 2D Ising model. Here, using agent-based Monte Carlo simulations, we study the Zaklan model with the well-known majority-vote model (MVM) with noise and apply it to tax evasion on ANs, to show that differently from the Ising model the MVM on ANs presents a well-defined phase transition. To control the tax evasion in the economics model proposed by Zaklan et al., MVM is applied in the neighborhood of the critical noise qc to the Zaklan model. Here we show that the Zaklan model is robust because this can also be studied, besides using equilibrium dynamics of Ising model, through the nonequilibrium MVM and on various topologies giving the same behavior regardless of dynamic or topology used here.

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32

MARQUÉS, MANUEL I., JULIO A. GONZALO, and JORGE ÍÑIGUEZ. "THERMALLY DILUTED ISING SYSTEMS." Fractals 11, supp01 (February 2003): 53–65. http://dx.doi.org/10.1142/s0218348x03001719.

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In this paper finite size scaling techniques are used to study the universality class of thermally diluted Ising systems, in which the realization of the disposition of magnetic atoms and vacancies is taken from the local distribution of spins in the pure original Ising model at criticality. The critical temperature, the critical exponents and therefore the universality class of these thermally diluted Ising systems depart markedly from the ones of short range correlated disordered systems. This result is in agreement with theoretical predictions previously made by Weinrib and Halperin for systems with long range correlated disorder.

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33

Zhang, Zhidong. "Mapping between Spin-Glass Three-Dimensional (3D) Ising Model and Boolean Satisfiability Problem." Mathematics 11, no. 1 (January 3, 2023): 237. http://dx.doi.org/10.3390/math11010237.

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The common feature for a nontrivial hard problem is the existence of nontrivial topological structures, non-planarity graphs, nonlocalities, or long-range spin entanglements in a model system with randomness. For instance, the Boolean satisfiability (K-SAT) problems for K ≥ 3 MSATK≥3 are nontrivial, due to the existence of non-planarity graphs, nonlocalities, and the randomness. In this work, the relation between a spin-glass three-dimensional (3D) Ising model MSGI3D with the lattice size N = mnl and the K-SAT problems is investigated in detail. With the Clifford algebra representation, it is easy to reveal the existence of the long-range entanglements between Ising spins in the spin-glass 3D Ising lattice. The internal factors in the transfer matrices of the spin-glass 3D Ising model lead to the nontrivial topological structures and the nonlocalities. At first, we prove that the absolute minimum core (AMC) model MAMC3D exists in the spin-glass 3D Ising model, which is defined as a spin-glass 2D Ising model interacting with its nearest neighboring plane. Any algorithms, which use any approximations and/or break the long-range spin entanglements of the AMC model, cannot result in the exact solution of the spin-glass 3D Ising model. Second, we prove that the dual transformation between the spin-glass 3D Ising model and the spin-glass 3D Z2 lattice gauge model shows that it can be mapped to a K-SAT problem for K ≥ 4 also in the consideration of random interactions and frustrations. Third, we prove that the AMC model is equivalent to the K-SAT problem for K = 3. Because the lower bound of the computational complexity of the spin-glass 3D Ising model CLMSGI3D is the computational complexity by brute force search of the AMC model CUMAMC3D, the lower bound of the computational complexity of the K-SAT problem for K ≥ 4 CLMSATK≥4 is the computational complexity by brute force search of the K-SAT problem for K = 3 CUMSATK=3. Namely, CLMSATK≥4=CLMSGI3D≥CUMAMC3D=CUMSATK=3. All of them are in subexponential and superpolynomial. Therefore, the computational complexity of the K-SAT problem for K ≥ 4 cannot be reduced to that of the K-SAT problem for K < 3.

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34

Song, Cui Ying, and Chuan Dong Li. "Simulation of Ising Model by Monte Carlo Method." Advanced Materials Research 936 (June 2014): 2271–75. http://dx.doi.org/10.4028/www.scientific.net/amr.936.2271.

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Simulating Ising model to calculate magnetization intensity by Monte Carlo method. The Ising model was introduced simply, sampled importantly, and calculated with programming. It shows the dependency relationship between the magnetization intensity and the size of dot-square line in different temperatures for Ising model. It cans edulcorate the approximation of analytic method by computer simulating. It obtains a method to appraise a model right or wrong by comparing the model and the experimental data.

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35

Chattopadhyay, Sourav, and S. B. Santra. "Study of diluted kinetic Ising model under sinusoidal external field." Journal of Physics: Conference Series 2207, no. 1 (March 1, 2022): 012005. http://dx.doi.org/10.1088/1742-6596/2207/1/012005.

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Abstract The ferromagnet to paramagnet phase transition temperature depends on the dilution concentration in the site diluted Ising ferromagnet. Though this model is a bistable system, few studies reported dynamic phase transition (DPT) in diluted Ising ferromagnet. We study dilution-dependent DPT in diluted Ising ferromagnet via Monte Carlo simulation under a time-varying external field tuning the system’s temperature on several system sizes. The nature of the transition is characterized by employing the finite-size scaling study.

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36

Litinskii, Leonid, and Boris Kryzhanovsky. "Inverse Problem for Ising Connection Matrix with Long-Range Interaction." Mathematics 9, no. 14 (July 9, 2021): 1624. http://dx.doi.org/10.3390/math9141624.

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In the present paper, we examine Ising systems on d-dimensional hypercube lattices and solve an inverse problem where we have to determine interaction constants of an Ising connection matrix when we know a spectrum of its eigenvalues. In addition, we define restrictions allowing a random number sequence to be a connection matrix spectrum. We use the previously obtained analytical expressions for the eigenvalues of Ising connection matrices accounting for an arbitrary long-range interaction and supposing periodic boundary conditions.

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37

KOLESÍK, M., and L. ŠAMAJ. "SOLVABLE CASES OF THE GENERAL SPIN-ONE ISING MODEL ON THE HONEYCOMB LATTICE." International Journal of Modern Physics B 06, no. 09 (May 10, 1992): 1529–38. http://dx.doi.org/10.1142/s0217979292000724.

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We consider a general spin-1 Ising model on the honeycomb lattice and propose a systematic method for obtaining its solvable cases. The method is based on a sequence of transformations which produces a path between the spin-1 and spin-½ Ising models. Considering necessary conditions for performing the transformations and the solvability of the resulting spin-½ system, we recover the known and find some new nontrivial ‘exactly solvable’ subspaces in the parameter space of the spin-1 Ising model.

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38

Campbell, Ian A., and Per H. Lundow. "Hyperscaling Violation in Ising Spin Glasses." Entropy 21, no. 10 (October 8, 2019): 978. http://dx.doi.org/10.3390/e21100978.

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In addition to the standard scaling rules relating critical exponents at second order transitions, hyperscaling rules involve the dimension of the model. It is well known that in canonical Ising models hyperscaling rules are modified above the upper critical dimension. It was shown by M. Schwartz in 1991 that hyperscaling can also break down in Ising systems with quenched random interactions; Random Field Ising models, which are in this class, have been intensively studied. Here, numerical Ising Spin Glass data relating the scaling of the normalized Binder cumulant to that of the reduced correlation length are presented for dimensions 3, 4, 5, and 7. Hyperscaling is clearly violated in dimensions 3 and 4, as well as above the upper critical dimension D = 6 . Estimates are obtained for the “violation of hyperscaling exponent” values in the various models.

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39

Dutta, Soham, and Andrew J. Gellman. "2D Ising Model for Enantiomer Adsorption on Achiral Surfaces: L- and D-Aspartic Acid on Cu(111)." Entropy 24, no. 4 (April 18, 2022): 565. http://dx.doi.org/10.3390/e24040565.

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The 2D Ising model is well-formulated to address problems in adsorption thermodynamics. It is particularly well-suited to describing the adsorption isotherms predicting the surface enantiomeric excess, ees, observed during competitive co-adsorption of enantiomers onto achiral surfaces. Herein, we make the direct one-to-one correspondence between the 2D Ising model Hamiltonian and the Hamiltonian used to describe competitive enantiomer adsorption on achiral surfaces. We then demonstrate that adsorption from racemic mixtures of enantiomers and adsorption of prochiral molecules are directly analogous to the Ising model with no applied magnetic field, i.e., the enantiomeric excess on chiral surfaces can be predicted using Onsager’s solution to the 2D Ising model. The implication is that enantiomeric purity on the surface can be achieved during equilibrium exposure of prochiral compounds or racemic mixtures of enantiomers to achiral surfaces.

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40

Bansal, N., S. Bravyi, and B. M. Terhal. "Classical approximation schemes for the ground-state energy of quantum and classical Ising spin Hamiltonians on planar graphs." Quantum Information and Computation 9, no. 7&8 (July 2009): 701–20. http://dx.doi.org/10.26421/qic9.7-8-12.

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We describe a classical approximation algorithm for evaluating the ground state energy of the classical Ising Hamiltonian with linear terms on an arbitrary planar graph. The running time of the algorithm grows linearly with the number of spins and exponentially with $1/\epsilon$, where $\epsilon$ is the worst-case relative error. This result contrasts the well known fact that exact computation of the ground state energy for the two-dimensional Ising spin glass model is NP-hard. We also present a classical approximation algorithm for the quantum Local Hamiltonian Problem or Quantum Ising Spin Glass problem on a planar graph {\em with bounded degree} which is known to be a QMA-complete problem. Using a different technique we find a classical approximation algorithm for the quantum Ising spin glass problem on the simplest planar graph with unbounded degree, the star graph.

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41

AGISHTEIN, M. E., and C. F. BAILLIE. "ISING MODEL SIMULATIONS ON THE MANIFOLDS OF TWO-DIMENSIONAL QUANTUM GRAVITY." Modern Physics Letters A 06, no. 17 (June 7, 1991): 1615–28. http://dx.doi.org/10.1142/s0217732391001755.

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The Ising model is stimulated on the manifolds of 2-dimensional quantum gravity, which are represented by fixed random triangulations (so-called quenched Ising model). Unlike the case of the Ising model on a dynamical random triangulation, there is no analytical prediction for the quenched case, since these manifolds do not have internal Hausdorff dimension and the problem cannot be formulated in matrix model language. The recursive sampling technique is used to generate the triangulations, lattice sizes being up to ten thousand triangles. The Metropolis algorithm was used for the spin update in order to obtain the initial estimation of the Curie point. After that we used the Wolff cluster algorithm in the critical region. We observed a second order phase transition, similar to that for the Ising model on a regular 2-dimensional lattice, and measured the critical exponents.

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42

Shi, Yuanyuan, and Bo Li. "Influence of Stress on the Chiral Polarization and Elastrocaloric Effect in BaTiO3 with 180° Domain Structure." Crystals 14, no. 6 (May 28, 2024): 511. http://dx.doi.org/10.3390/cryst14060511.

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The polarization and elastrocaloric effect of chiral barium titanate (BaTiO3) with an Ising–Bloch-type domain wall under stress was investigated using the Landau–Ginzburg–Devonshire (LGD) theory. It has been shown that tensile stresses increase the magnitude of the Ising polarization component in barium titanate, together with a decrease in the domain wall width. Compressive stresses cause a reduction in the Ising polarization component and an increase in the domain width. Under compressive stress, barium titanate exhibits a negative elastrocaloric effect and temperature changes with increasing stress, while BaTiO3 exhibits a positive elastrocaloric effect under tensile stress. Bloch polarization shows angle-dependent polarization under external force, but the temperature change from the elastrocaloric effect is smaller than that of Ising polarization under stress. This work contributes to the understanding of polarization evolution under tension in ferroelectrics with chiral structure.

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43

Lisnyi, B. M. "Distorted Diamond Ising–Hubbard Chain in the Special Limit of Infinite On-Site Repulsion." Ukrainian Journal of Physics 69, no. 10 (October 29, 2024): 732. http://dx.doi.org/10.15407/ujpe69.10.732.

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The exact solution of the distorted diamond Ising–Hubbard chain is analyzed in the special limit of infinite on-site electron-electron repulsion, where the two-electron Hubbard dimer becomes equivalent to the antiferromagnetic isotropic Heisenberg dimer. The special limit of infinite repulsion for the matrix of the cell Hamiltonian of this model is analytically calculated, and it is demonstrated that the exact solution of the distorted diamond Ising–Hubbard chain in this limit coincides with the exact solution of the spin-1/2 distorted diamond Ising–Heisenberg chain with antiferromagnetic isotropic Heisenberg interaction. The numerical calculation of the special limit of infinite repulsion for the ground-state phase diagram and thermodynamic characteristics of the distorted diamond Ising–Hubbard chain was performed in a way that provides a very fast convergence to the limit results for these characteristics.

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44

Daskalakis, Constantinos, Nishanth Dikkala, and Gautam Kamath. "Testing Ising Models." IEEE Transactions on Information Theory 65, no. 11 (November 2019): 6829–52. http://dx.doi.org/10.1109/tit.2019.2932255.

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45

Durhuus, B., and G. M. Napolitano. "Generic Ising trees." Journal of Physics A: Mathematical and Theoretical 45, no. 18 (April 24, 2012): 185004. http://dx.doi.org/10.1088/1751-8113/45/18/185004.

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46

Balbuena, P., and K. A. Dawson. "Extended Ising model." Physical Review B 38, no. 16 (December 1, 1988): 11432–43. http://dx.doi.org/10.1103/physrevb.38.11432.

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47

Creutz, Michael. "Deterministic ising dynamics." Annals of Physics 167, no. 1 (March 1986): 62–72. http://dx.doi.org/10.1016/s0003-4916(86)80006-9.

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48

Johnston, D. A., and Ranasinghe P. K. C. Malmini. "Gonihedric Ising actions." Nuclear Physics B - Proceedings Supplements 53, no. 1-3 (February 1997): 773–76. http://dx.doi.org/10.1016/s0920-5632(96)00778-5.

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49

Hystad, Grethe. "Periodic Ising Correlations." Journal of Mathematical Physics 52, no. 1 (January 2011): 013302. http://dx.doi.org/10.1063/1.3517425.

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Zamolodchikov, Al B. "From tricritical Ising to critical Ising by thermodynamic Bethe ansatz." Nuclear Physics B 358, no. 3 (July 1991): 524–46. http://dx.doi.org/10.1016/0550-3213(91)90423-u.

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