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Journal articles on the topic 'Critical exponent'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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1

JANSSEN, MARTIN. "MULTIFRACTAL ANALYSIS OF BROADLY-DISTRIBUTED OBSERVABLES AT CRITICALITY." International Journal of Modern Physics B 08, no. 08 (1994): 943–84. http://dx.doi.org/10.1142/s021797929400049x.

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The multifractal analysis of disorder-induced localization-delocalization transitions is reviewed. Scaling properties of this transition are generic for multi parameter coherent systems which show broadly-distributed observables at criticality. The multifractal analysis of local measures is extended to more general observables including scaling variables such as the conductance in the localization problem. The relation of multifractal dimensions to critical exponents such as the order parameter exponent β and the correlation length exponent ν is investigated, We discuss a number of scaling rel

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2

Wang, Zejia, Jingxue Yin, and Chunpeng Wang. "Large-time behaviour of solutions to non-Newtonian filtration equations with nonlinear boundary sources." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 140, no. 4 (2010): 833–55. http://dx.doi.org/10.1017/s0308210509000675.

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This paper deals with the large-time behaviour of solutions to the exterior problem of the non-Newtonian filtration equation with first-order term and nonlinear boundary source. In particular, the critical global exponent and the critical Fujita exponent are determined or estimated. An interesting phenomenon is shown: there exists a threshold value for the coefficient of the first-order term such that the critical global exponent is strictly less than the critical Fujita exponent when the coefficient is under this threshold, while these two exponents are identically equal when the coefficient

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3

Łukiewska, Agnieszka, and Piotr Gębara. "Structure, Magnetocaloric Effect and Critical Behavior of the Fe60Co12Gd4Mo3B21 Amorphous Ribbons." Materials 15, no. 1 (2021): 34. http://dx.doi.org/10.3390/ma15010034.

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The aim of the paper was to study the structure, magnetic properties and critical behavior of the Fe60Co12Gd4Mo3B21 alloy. The X-ray diffractometry and the Mössbauer spectroscopy studies confirmed amorphous structure. The analysis of temperature evolution of the exponent n (ΔSM = C·(Bmax)n) and the Arrott plots showed the second order phase transition in investigated material. The analysis of critical behavior was carried out in order to reveal the critical exponents and precise TC value. The ascertained critical exponents were used to determine the theoretical value of the exponent n, which c

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4

Naveena Kumara, A., Shreyas Punacha, and Md Sabir Ali. "Lyapunov exponents and phase structure of Lifshitz and hyperscaling violating black holes." Journal of Cosmology and Astroparticle Physics 2024, no. 07 (2024): 061. http://dx.doi.org/10.1088/1475-7516/2024/07/061.

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Abstract We study the phase structure of Lifshitz and hyperscaling violating (HSV) black holes using Lyapunov exponents. For describing hyperscaling violating system, we chose a particular gravity model constructed from generalized Einstein-Maxwell-Dilaton action which includes the Lifshitz cases at appropriate limits. We study the relationship between Lyapunov exponents and black hole phase transitions considering both the timelike and null geodesics. We observe that, the black hole phase transiton properties are reflected in Lyapunov exponent where its multiple branches correspond to the dis

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5

Kim, M. O., Hoyun Lee, Chil-Min Kim, Hyun-Soo Pang, Eok-Kyun Lee, and O. J. Kwon. "New Characteristic Relations in Type-II and III Intermittency." International Journal of Bifurcation and Chaos 07, no. 04 (1997): 831–36. http://dx.doi.org/10.1142/s0218127497000613.

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We obtained new characteristic relations in Type-II and III intermittencies according to the reinjection probability distribution. When the reinjection probability distribution is fixed at the lower bound of reinjection, the critical exponents are -1, as is well known. However when the reinjection probability distribution is uniform, the critical exponent is -1/2, and when it is of form [Formula: see text], -3/4. On the other hand, if the square root of Δ, which represents the lower bound of reinjection, is much smaller than the control parameter ∊, i.e. ∊ ≫ Δ1/2, critical exponent is always -

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6

SIMÕES, C. S., and J. R. DRUGOWICH DE FELÍCIO. "DYNAMIC CRITICAL EXPONENTS OF THE ISING MODEL WITH MULTISPIN INTERACTIONS." Modern Physics Letters B 15, no. 15 (2001): 487–96. http://dx.doi.org/10.1142/s0217984901001902.

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We revisit the short-time dynamics of 2D Ising model with three spin interactions in one direction and estimate the critical exponents z, θ, β and ν. Taking properly into account the symmetry of the Hamiltonian, we obtain results completely different from those obtained by Wang et al.10 For the dynamic exponent z our result coincides with that of the 4-state Potts model in two dimensions. In addition, results for the static exponents ν and β agree with previous estimates obtained from finite size scaling combined with conformal invariance. Finally, for the new dynamic exponent θ we find a nega

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7

Qianze, Liu, He Wenping, Xie Xiaoqiang, Mei Ying, Sun Hui, and Boers Niklas. "Early warning signal of abrupt change in sea level pressure based on changing spectral exponent." Chaos, Solitons and Fractals 187 (November 13, 2024): 115350. https://doi.org/10.5281/zenodo.14141308.

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<strong>A</strong><strong>bst</strong><strong>r</strong><strong>act</strong> When a complex system crosses its critical points, abrupt change will occur with potentially catastrophic consequences. It is therefore crucial to investigate early warning signals for such transitions. Some studies show that the changing spectral exponent could serve as an early warning signal, as a dynamical system approaches its critical transition point. However, the performance of the spectral exponent may be influenced by different bifurcation types and spectral estimation techniques. We therefore first test the

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8

Skal, Asya S. "Fractons with Scalar and Vector Interactions and Two Scaling Relations between the Static and Dynamic Critical Exponents." Modern Physics Letters B 12, no. 12 (1998): 467–74. http://dx.doi.org/10.1142/s0217984998000573.

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Using new equilibrium equation [PhysicaA242, 13 (1997)] and Einstein's relation, new critical exponents for Young modulus Y(p)∝(p-p c )2t-g and regular diffusion [Formula: see text] are introduced, where t is the conductivity critical exponent and g=0.6 is the Hall coefficient critical exponent above the threshold. These results allows us to introduce two superuniversal fractons dimensions: with the scalar displacements d s =4/3 (the Alexander and Orbach conjecture) and with the vector displacements d v =21/20) which leads to new scaling relations between the static and dynamic critical expone

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9

Corona, Dario, and Alessandro Della Corte. "The critical exponent functions." Comptes Rendus. Mathématique 360, G4 (2022): 315–32. http://dx.doi.org/10.5802/crmath.286.

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10

Corona, Dario, and Alessandro Della Corte. "The critical exponent functions." Comptes Rendus. Mathématique 360, G4 (2022): 315–32. http://dx.doi.org/10.5802/crmath.286.

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11

Berg, Robert F., and Michael R. Moldover. "Critical exponent for viscosity." Physical Review A 42, no. 12 (1990): 7183–86. http://dx.doi.org/10.1103/physreva.42.7183.

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12

Su, Jiabao, and Cong Wang. "Weighted critical exponents of Sobolev-type embeddings for radial functions." Advanced Nonlinear Studies 22, no. 1 (2022): 143–58. http://dx.doi.org/10.1515/ans-2022-0006.

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Abstract In this article, we prove the upper weighted critical exponents for some embeddings from weighted Sobolev spaces of radial functions into weighted Lebesgue spaces. We also consider the lower critical exponent for certain embedding.

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13

Luo, H. J., and B. Zheng. "Critical Relaxation and Critical Exponents." Modern Physics Letters B 11, no. 14 (1997): 615–23. http://dx.doi.org/10.1142/s0217984997000761.

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Dynamic relaxation of the XY model and fully frustrated XY model quenched from an initial ordered state to the critical temperature or below is investigated with Monte Carlo methods. Universal power law scaling behavior is observed. The dynamic critical exponent z and the static exponent η are extracted from the time-dependent Binder cumulant and magnetization. The results are competitive to those measured with traditional methods.

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14

Tsouli, Najib, Mustapha Haddaoui, and El Miloud Hssini. "Multiple solutions for a critical $p(x)$-Kirchhoff type equations." Boletim da Sociedade Paranaense de Matemática 38, no. 4 (2019): 197–211. http://dx.doi.org/10.5269/bspm.v38i4.37697.

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In this paper, by using the concentration--compactness principle of Lions for variable exponents and variational arguments, we obtain the existence and multiplicity solutions for a class of $p(x)$-Kirchhoff type equations with critical exponent.

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15

Singh, Rohit, and Sanjay Puri. "Strain fields and critical phenomena in manganites II: spin-lattice-energy Hamiltonians." Journal of Statistical Mechanics: Theory and Experiment 2023, no. 3 (2023): 033206. http://dx.doi.org/10.1088/1742-5468/acc065.

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Abstract The dynamic critical behavior at the paramagnetic-antiferromagnetic (PM-AFM) transition in manganites has recently been studied experimentally (Niermann et al 2015 Phys. Rev. Lett. 114 037204). We extend the Hamiltonian of paper I by incorporating an energy field, and study the corresponding Model C of critical dynamics. We use the dynamic renormalization group approach and calculate the dynamic critical exponents z, ν z and the line-width exponent Δ to leading order in the small expansion parameters ϵ = 4 − d + 2 σ and ϵ ′ = 4 − d . Here, d is the space dimension and σ is the long-ra

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16

ALVES, NELSON, and JOSÉ ROBERTO DRUGOWICH DE FELÍCIO. "SHORT-TIME DYNAMIC EXPONENTS OF AN ISING MODEL WITH COMPETING INTERACTIONS." Modern Physics Letters B 17, no. 05n06 (2003): 209–18. http://dx.doi.org/10.1142/s0217984903005068.

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In this work the two-dimensional Ising model with nearest- and next-nearest-neighbor interactions is revisited. We obtain the dynamic critical exponents z and θ from short-time Monte Carlo simulations. The dynamic critical exponent z is obtained from the time behavior of the ratio [Formula: see text], whereas the non-universal exponent θ is estimated from the time correlation of the order parameter <M(0)M(t)> ~ tθ, where M(t) is the order parameter at instant t, d is the dimension of the system and <(⋯)> is the average of the quantity (⋯) over different samples. We also obtain the

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17

Дзюба, Ж. В., та В. Н. Удодов. "Критический индекс восприимчивости 1D-изинговского ферромагнетика, замкнутого в кольцо". Физика твердого тела 60, № 7 (2018): 1318. http://dx.doi.org/10.21883/ftt.2018.07.46115.238.

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AbstractUsing the Monte Carlo method, critical behavior of the one-dimensional ferromagnetic Ising model has been investigated with allowance for the interaction of the second and third neighbors and four-particle interaction. The obtained results on the critical temperature were compared with the critical temperature of the quasi-one-dimensional Ising magnetic [(СН_3)_3NH] · FeCl_3 · 2H_2O and with the magnitude of the exchange interaction J/k _B = 17.4 K. Within the scope of the finite-dimensional scaling theory, the critical susceptibility exponent has been calculated. It has been shown tha

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18

Alencar, D. S. M., T. F. A. Alves, G. A. Alves, F. W. S. Lima, A. Macedo-Filho, and R. S. Ferreira. "Two-dimensional diffusive epidemic process in the presence of quasiperiodic and quenched disorder." Journal of Statistical Mechanics: Theory and Experiment 2023, no. 4 (2023): 043205. http://dx.doi.org/10.1088/1742-5468/acc64d.

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Abstract This work considers the diffusive epidemic process model coupled to the square lattice, the Penrose quasiperiodic lattice, and the Voronoi–Delaunay random lattice. The main objective is to verify if spatial disorder influences critical behavior. According to the Harris–Barghathi–Vojta criterion, quenched or quasiperiodic disorder can change the critical behavior of the system, depending on the disorder decay exponent of the lattice. We employed extensive Monte Carlo simulations of the relevant quantities. Furthermore, we estimate the critical exponent ratios. Our results suggest that

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19

Ho, Ky, та Yun-Ho Kim. "The concentration-compactness principles for Ws,p(·,·)(ℝN) and application". Advances in Nonlinear Analysis 10, № 1 (2020): 816–48. http://dx.doi.org/10.1515/anona-2020-0160.

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Abstract We obtain a critical imbedding and then, concentration-compactness principles for fractional Sobolev spaces with variable exponents. As an application of these results, we obtain the existence of many solutions for a class of critical nonlocal problems with variable exponents, which is even new for constant exponent case.

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20

BULDYREV, SERGEY V., SHLOMO HAVLIN, JANOS KERTÉSZ, ARKADY SHEHTER, and H. EUGENE STANLEY. "SURFACE ROUGHENING WITH QUENCHED DISORDER IN d-DIMENSIONS." Fractals 01, no. 04 (1993): 827–39. http://dx.doi.org/10.1142/s0218348x9300085x.

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We review recent numerical simulations of several models of interface growth in d- dimensional media with quenched disorder. These models belong to the universality class of anisotropic diode-resistor percolation networks. The values of the roughness exponent α=0.63±0.01 (d=1+1) and α=0.48±0.02 (d=2+1) are in good agreement with our recent experiments. We study also the diode-resistor percolation on a Cayley tree. We find that [Formula: see text] thus suggesting that the critical exponent for [Formula: see text]βp=∞ and that the upper critical dimension in this problem is d=dc=∞. Other critica

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21

Yurtseven, H., and S. Aksoy. "Analysis of the magnetization and the inverse susceptibility near the Curie temperature in double perovskite." Low Temperature Physics 51, no. 3 (2025): 361–67. https://doi.org/10.1063/10.0035841.

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The temperature dependences of the magnetization M and the inverse susceptibility χ–1 are analyzed by the power-law formulae with the critical exponent's order parameter β and susceptibility γ, respectively, for the double perovskites R2NiMnO6 (R = Dy, Ho, and Er) close to the ferromagnetic–paramagnetic (FM–PM) transition using the literature data. Values of the critical exponents β and γ are also determined by the Kouvel–Fisher method near the Curie temperature TC for the FM–PM transition in those double perovskites. Additionally, the magnetic field H dependence of the magnetization M is anal

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22

Dai, Peihua, Youzhu Zhang, and M. P. Sarachik. "Critical conductivity exponent for Si:B." Physical Review Letters 66, no. 14 (1991): 1914–17. http://dx.doi.org/10.1103/physrevlett.66.1914.

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23

Strydom, A. M., P. de V. du Plessis, D. Kaczorowski та R. Troć. "Critical exponent β of U3P4". Physica B: Condensed Matter 186-188 (травень 1993): 785–87. http://dx.doi.org/10.1016/0921-4526(93)90704-a.

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24

Strydom, A. M., P. de V. du Plessis, R. Troć та D. Kaczorowski. "Critical exponent β of U3As4". Journal of Magnetism and Magnetic Materials 140-144 (лютий 1995): 1429–30. http://dx.doi.org/10.1016/0304-8853(94)00603-2.

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25

Veitsblit, A. I. "Norms possessing a critical exponent." Ukrainian Mathematical Journal 38, no. 5 (1987): 551–53. http://dx.doi.org/10.1007/bf01060951.

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26

Hatefi, Armin, Ehsan Hatefi, and Roberto J. Lopez-Sastre. "Neural networks assisted Metropolis-Hastings for Bayesian estimation of critical exponent on elliptic black hole solution in 4D using quantum perturbation theory." Journal of Cosmology and Astroparticle Physics 2024, no. 09 (2024): 015. http://dx.doi.org/10.1088/1475-7516/2024/09/015.

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Abstract It is well-known that the critical gravitational collapse produces continuous self-similar solutions characterized by the Choptuik critical exponent, γ. We examine the solutions in the domains of the linear perturbation equations, considering the numerical measurement errors. Specifically, we study quantum perturbation theory for the four-dimensional Einstein-axion-dilaton system of the elliptic class of SL(2,ℝ) transformations. We develop a novel artificial neural network-assisted Metropolis-Hastings algorithm based on quantum perturbation theory to find the distribution of the criti

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27

Jang, Hoseung, Mouhcine Azhari, and Unjong Yu. "Monte Carlo study for the thermodynamic and dynamic phase transitions in the spin-S Ising model on Sierpiński carpet." Journal of Statistical Mechanics: Theory and Experiment 2024, no. 1 (2024): 013201. http://dx.doi.org/10.1088/1742-5468/ad0a91.

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Abstract We study the thermodynamic and dynamic phase transitions (TPT and DPT) of the spin- 1 / 2 and spin-1 Ising models on three graphs constructed on the Sierpiński carpet. This study employs Monte Carlo methods, specifically the Wolff and Metropolis algorithms, in conjunction with finite-size scaling analysis. By calculating the critical temperature and critical exponent ratio γ / ν associated with the TPT, we demonstrate that the three graphs exhibit an identical critical exponent ratio for both the spin- 1 / 2 and spin-1 Ising models within statistical error. Furthermore, we explore the

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28

SCHAEFFER, LUKE, and JEFFREY SHALLIT. "THE CRITICAL EXPONENT IS COMPUTABLE FOR AUTOMATIC SEQUENCES." International Journal of Foundations of Computer Science 23, no. 08 (2012): 1611–26. http://dx.doi.org/10.1142/s0129054112400655.

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The critical exponent of an infinite word is defined to be the supremum of the exponent of each of its factors. For k-automatic sequences, we show that this critical exponent is always either a rational number or infinite, and its value is computable. Our results also apply to variants of the critical exponent, such as the initial critical exponent of Berthé, Holton, and Zamboni and the Diophantine exponent of Adamczewski and Bugeaud. Our work generalizes or recovers previous results of Krieger and others, and is applicable to other situations; e.g., the computation of the optimal recurrence c

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29

Frank, Trefoily. "Critical Line in the Euler–Riemann Zeta Function." Annals of Mathematics and Physics 8, no. 2 (2025): 057–59. https://doi.org/10.17352/amp.000146.

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This study focused on the transformation of an exponentially growing divergent function sin(Rln(x)) into a convergent function by its complementary exponential function xt in such a manner that the sizes of positive and negative areas under sin would be the same. The transformation will provide the entire sin function with self-compensatory behavior. The exponent's value was computed and found to be -1/2 , which is the only exponent, which lets entire product of the function converge to zero (sum of area for positive real numbers and sum of products for natural numbers). The exponent -1/2 is a

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30

Nenuwe, Nelson, and John O. A. Idiodi. "Momentum Distribution Critical Exponents for 1D Hubbard model in a Magnetic Field." JOURNAL OF ADVANCES IN PHYSICS 11, no. 3 (2015): 3091–98. http://dx.doi.org/10.24297/jap.v11i3.468.

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Critical exponents at Â and Â Â for the momentum distribution function are studied for one-dimensional Hubbard model in the presence of magnetic field, using conformal field theory (CFT) approach. Exponents at Â and Â are reproduced. Results at Â is in contrast to earlier numerical prediction of 1, while at , the exponent is 49/8. The singularities at Â and Â appears to be weak and gradually degenerating into a smooth curve.

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31

Belim, S. V. "Critical Behaviour in Systems in which Long-Range and Short-Range Forces Compete." Herald of the Bauman Moscow State Technical University. Series Natural Sciences, no. 82 (2019): 37–47. http://dx.doi.org/10.18698/1812-3368-2019-1-37-47.

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Critical behaviour of a range of ferromagnetic materials deviates from the predictions of the Ising, XY and Heisenberg models. Additional long-range forces competing with regular exchange interaction may explain this deviation. These competing interactions lead to new universality classes of critical behaviour. The paper uses the field theory approach to investigate critical behaviour in those systems in which long-range and short-range forces compete. We consider the case when a power function of distance r-D-σ, when 1.5 < σ < 2.0, can describe the long-range forces. There exists a dist

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32

Nie, Yuanyuan, Yan Leng, Xu Zhao, and Qian Zhou. "Critical Fujita exponents for a class of quasilinear coupled parabolic equations." Electronic Journal of Differential Equations 2025, no. 01-?? (2025): 21. https://doi.org/10.58997/ejde.2025.21.

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This article concerns the critical Fujita exponents for a class of quasilinear coupled parabolic equations. Using energy estimates, suitable supersolutions, and the comparison principle, the blow-up theorem of Fujita type is established, and the critical Fujita exponent is obtained. Furthermore, we show that the critical case belongs to the blow-up case. For more information see https://ejde.math.txstate.edu/Volumes/2025/21/abstr.html

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33

El Hamidi, Abdallah, and Mokhtar Kirane. "Nonexistence results of solutions to systems of semilinear differential inequalities on the Heisenberg group." Abstract and Applied Analysis 2004, no. 2 (2004): 155–64. http://dx.doi.org/10.1155/s108533750430802x.

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We establish nonexistence results to systems of differential inequalities on the(2N+1)-Heisenberg group. The systems considered here are of the type(ESm). These nonexistence results hold forNless than critical exponents which depend onpiandγi,1≤i≤m. Our results improve the known estimates of the critical exponent.

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Yang, Shaojie, Jun Tao, Benrong Mu, and Aoyun He. "Lyapunov exponents and phase transitions of Born-Infeld AdS black holes." Journal of Cosmology and Astroparticle Physics 2023, no. 07 (2023): 045. http://dx.doi.org/10.1088/1475-7516/2023/07/045.

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Abstract In this paper, we characterize the phase transitons of Born-Infeld AdS black holes in terms of Lyapunov exponents. We calculate the Lyapunov exponents for timelike geodesics in background metric and photon geodesics in effective metric. It is found that black hole phase transitions can be described by multiple-valued Lyapunov exponents. And its phase diagram can be characterized by Lyapunov exponents and Hawking temperature. Besides, the change of Lyapunov exponents can be considered as order parameter, and exists a critical exponent 1/2 near critical point.

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Zheng, B. "Monte Carlo Simulations of Short-Time Critical Dynamics." International Journal of Modern Physics B 12, no. 14 (1998): 1419–84. http://dx.doi.org/10.1142/s021797929800288x.

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Monte Carlo simulations of the short-time critical dynamics are reviewed. The short-time universal scaling behavior of the dynamic Ising model and Potts model are discussed in detail, while extension and application to more complex systems as the XY model, the fully frustrated XY model and other dynamic systems are also presented. The investigation of the universal behavior of the short-time dynamics not only enlarges the fundamental knowledge on critical phenomena but also, more interestingly, provides possible new ways to determine not only the new critical exponents θ and θ1, but also the t

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HÜLLER, ALFRED, and MICHEL PLEIMLING. "MICROCANONICAL DETERMINATION OF THE ORDER PARAMETER CRITICAL EXPONENT." International Journal of Modern Physics C 13, no. 07 (2002): 947–56. http://dx.doi.org/10.1142/s0129183102003693.

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A highly efficient Monte Carlo method for the calculation of the density of states of classical spin systems is presented. As an application, we investigate the density of states ΩN(E, M) of two- and three-dimensional Ising models with N spins as a function of energy E and magnetization M. For a fixed energy lower than a critical value Ec,N the density of states exhibits two sharp maxima at M = ± Msp(E) which define the microcanonical spontaneous magnetization. An analysis of the form Msp(E) ∝ (Ec, ∞ - E)βε yields very good results for the critical exponent βε, thus demonstrating that critical

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37

Ferrero, E. E., and E. A. Jagla. "Criticality in elastoplastic models of amorphous solids with stress-dependent yielding rates." Soft Matter 15, no. 44 (2019): 9041–55. http://dx.doi.org/10.1039/c9sm01073d.

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Elastoplastic models are analyzed at the yielding transition. Universality and critical exponents are discussed. The flowcurve exponent happens to be sensitive to the local yielding rule. An alternative mean-field description of yielding is explained.

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38

Liu, Shuo, Erica W. Carlson, and Karin A. Dahmen. "Connecting Complex Electronic Pattern Formation to Critical Exponents." Condensed Matter 6, no. 4 (2021): 39. http://dx.doi.org/10.3390/condmat6040039.

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Scanning probes reveal complex, inhomogeneous patterns on the surface of many condensed matter systems. In some cases, the patterns form self-similar, fractal geometric clusters. In this paper, we advance the theory of criticality as it pertains to those geometric clusters (defined as connected sets of nearest-neighbor aligned spins) in the context of Ising models. We show how data from surface probes can be used to distinguish whether electronic patterns observed at the surface of a material are confined to the surface, or whether the patterns originate in the bulk. Whereas thermodynamic crit

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39

Su, Yu, and Hongxia Shi. "Quasilinear Choquard equation with critical exponent." Journal of Mathematical Analysis and Applications 508, no. 1 (2022): 125826. http://dx.doi.org/10.1016/j.jmaa.2021.125826.

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40

Richomme, Gwenaël. "Minimal critical exponent of quasiperiodic words." Theoretical Computer Science 548 (September 2014): 117–22. http://dx.doi.org/10.1016/j.tcs.2014.06.039.

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41

Sorensen, C. M. "Critical exponent doubling in microemulsion systems." Chemical Physics Letters 117, no. 6 (1985): 606–8. http://dx.doi.org/10.1016/0009-2614(85)80310-9.

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42

Sengers, Jan V., and Joseph G. Shanks. "Experimental Critical-Exponent Values for Fluids." Journal of Statistical Physics 137, no. 5-6 (2009): 857–77. http://dx.doi.org/10.1007/s10955-009-9840-z.

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43

Adimurthi, P. N. Srikanth та S. L. Yadava. "Phenomena of critical exponent in ℝ2". Proceedings of the Royal Society of Edinburgh: Section A Mathematics 119, № 1-2 (1991): 19–25. http://dx.doi.org/10.1017/s0308210500028274.

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SynopsisIn this paper we make an attempt to explain the critical phenomena in ℝ2. We do this by exhibiting a class of functions having growth and for whichdo not admit a solution when R is sufficiently small, where B(R) denotes the ball of radius R in ℝ2.

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Barrańón, A., R. Cárdenas, C. O. Dorso, and al et. "The Critical Exponent of Nuclear Fragmentation." Acta Physica Hungarica A) Heavy Ion Physics 17, no. 1 (2003): 59–73. http://dx.doi.org/10.1556/aph.17.2003.1.8.

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Gautam, S. Zubin. "A critical-exponent Balian–Low theorem." Mathematical Research Letters 15, no. 3 (2008): 471–83. http://dx.doi.org/10.4310/mrl.2008.v15.n3.a7.

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Newman, C. M. "Some critical exponent inequalities for percolation." Journal of Statistical Physics 45, no. 3-4 (1986): 359–68. http://dx.doi.org/10.1007/bf01021076.

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Liu, Beibei, and Shi Wang. "Discrete subgroups of small critical exponent." Geometry & Topology 27, no. 6 (2023): 2347–81. http://dx.doi.org/10.2140/gt.2023.27.2347.

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Corona, Dario, and Alessandro Della Corte. "Corrigendum to “The critical exponent functions”." Comptes Rendus. Mathématique 363, G8 (2025): 791–92. https://doi.org/10.5802/crmath.667.

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WEBER, H., D. BECKMANN, J. WOSNITZA, H. v. LÖHNEYSEN, and D. VISSER. "INFLUENCE OF CHIRAL SYMMETRY ON THE CRITICAL BEHAVIOR OF STACKED TRIANGULAR ANTIFERROMAGNETS." International Journal of Modern Physics B 09, no. 12 (1995): 1387–407. http://dx.doi.org/10.1142/s0217979295000604.

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Abstract:

We review and extend our recent specific-heat results of three antiferromagnetic quasi-onedimensional magnets, CsMnBr 3, CsNiCl 3, and CsMnI 3, with chiral symmetry. In zero field, CsMnBr 3 exhibits an unusually large critical specific-heat exponent α in good agreement with predictions for chiral XY symmetry. The anisotropy-crossover exponent ɸ has been determined in low fields applied perpendicular to the c axis. ɸ is clearly smaller than unity and differs from theoretical predictions. For CsNiCl 3 we find a crossover in fields B||c from conventional universality behavior for B=0 to chiral He

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NASSIF, CLÁUDIO, and P. R. SILVA. "A+B→0 ENHANCED DIFFUSION-CONTROLLED REACTIONS UNDER STATIONARY REGIME CONDITION THROUGH THOMPSON'S APPROACH." Modern Physics Letters B 18, no. 09 (2004): 345–53. http://dx.doi.org/10.1142/s0217984904006937.

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Abstract:

In this work, Thompson's method is used to study the A+B→0 reactions controlled by anomalous and brownian diffusion in the case of an external homogeneous source (h) of particles A and B under sthequiometric condition (the same input rate h) and also in the special case of the stationary regime. So the novelty in the present work is that we are able to obtain for such kind of reactions (σ=1) the static critical exponent δ of concentration [Formula: see text], the dynamical exponent for the relaxation time Δ'(τh~h-Δ') and the exponent for the concentration decaying ξ(∊~τ-ξ), with all these quan

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