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Journal articles on the topic 'Axial next-nearest-neighbor Ising (ANNNI) model'

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Published: 4 June 2021
Last updated: 1 February 2022

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1

Randa, J. "Axial next-nearest-neighbor Ising (ANNNI) and extended-ANNNI models in external fields." Physical Review B 32, no. 1 (July 1, 1985): 413–16. http://dx.doi.org/10.1103/physrevb.32.413.

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2

Randa, J. "Erratum: Axial next-nearest-neighbor Ising (ANNNI) and extended-ANNNI models in external fields." Physical Review B 33, no. 3 (February 1, 1986): 2020. http://dx.doi.org/10.1103/physrevb.33.2020.2.

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3

Nakanishi, Kazuo. "Nonlinear Effect on the Axial Next-Nearest Neighbor Ising (ANNNI) Model: Application to CeSb." Journal of the Physical Society of Japan 58, no. 4 (April 1989): 1296–306. http://dx.doi.org/10.1143/jpsj.58.1296.

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4

Nakanishi, Kazuo. "Absence of Partially Disordered States in the Axial Next Nearest-Neighbor Ising (ANNNI) Model." Journal of the Physical Society of Japan 61, no. 8 (August 15, 1992): 2901–8. http://dx.doi.org/10.1143/jpsj.61.2901.

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5

Nakanishi, Kazuo. "Nonlinear Effect on the Axial Next-Nearest Neighbor Ising (ANNNI) Model. II. Application to CeBi." Journal of the Physical Society of Japan 59, no. 8 (August 15, 1990): 2986–94. http://dx.doi.org/10.1143/jpsj.59.2986.

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6

Akai Kurbanovich, Murtazaev, and Ibaev Zhavrail Gadzhievich. "The Monte Carlo simulation of 2D ANNNI-model." EPJ Web of Conferences 185 (2018): 11010. http://dx.doi.org/10.1051/epjconf/201818511010.

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In this, study we present the data for 2D Axial Next Nearest Neighbor Ising model (ANNNI-model) obtained from Monte Carlo (MC) simulations using the standard Metropolis algorithm. The temperature dependences of thermodynamic parameters for a cubic lattice with linear sizes L=32 at different values of the competing interaction parameter |J1/J|=0.1÷1.0. Transition temperatures of ferromagnetic ordering to the paramagnetic state at |J1/J|<0.3 and to the modulated state at 0.3<|J1/J|<0.5 are shown to shift towards low temperatures with an increase in a competing interaction parameter absolute value. Conversely, transition temperatures of the modulate state to the paramagnetic ordering grow. The modulated ordering in the 2D ANNNImodel appears in the temperature range 0.1<T<2.0 at 0.2<|J1/J|≤1.0. Modulated structure parameters are computed using a mathematic apparatus of Fourier transform spectral analysis. According to the Fourier analysis results, the wave number grows with an increase in the competing interaction parameter absolute value. Summarizing obtained results, we plot a phase diagram of 2D anisotropic Ising model with competing interactions.
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7

SEN, P., and B. K. CHAKRABARTI. "FRUSTRATED TRANSVERSE ISING MODELS: A CLASS OF FRUSTRATED QUANTUM SYSTEMS." International Journal of Modern Physics B 06, no. 14 (July 20, 1992): 2439–69. http://dx.doi.org/10.1142/s0217979292001237.

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The analytical and numerical (Monte Carlo and exact diagonalisation) estimates of phase diagrams of frustrated Ising models in transverse fields are discussed here. Specifically we discuss the Sherrington–Kirkpatrick model in transverse field and the Axial Next-Nearest Neighbour Ising (ANNNI) model in transverse field. The effects of quantum fluctuations (induced by the transverse field) on the ground and excited states of such systems with competing interactions (frustration) are also discussed. The results are compared to those available for other frustrated quantum systems.
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8

Muraoka, Y., M. Ochiai, T. Idogaki, and N. Uryu. "S=1 axial next-nearest neighbour Ising (ANNNI) model with higher order spin interaction." Journal of Physics A: Mathematical and General 26, no. 8 (April 21, 1993): 1811–21. http://dx.doi.org/10.1088/0305-4470/26/8/010.

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9

Price, Geoffrey D., and Julia Yeomans. "A model for polysomatism." Mineralogical Magazine 50, no. 355 (March 1986): 149–56. http://dx.doi.org/10.1180/minmag.1986.050.355.20.

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AbstractWe show that the structures and phases developed in a variety of polysomatic series, including the biopyroboles, are similar to those predicted by a simple spin model—the Axial Next-Nearest-Neighbour Ising (ANNNI) model in a magnetic field. We argue that the different polysomatic structures can be considered as thermodynamically stable phases, composed of ordered sequences of chemically distinct structural modules. We suggest that the key factors which determine the stability of polysomatic phases are (a) the chemical potential, which controls the proportion of the different structural modules, and (b) the competing interactions between first and second neighbour modules within the structures.
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10

Muraoka, Y., M. Ochiai, and T. Idogaki. "Magnetic phase diagram of the S=1 axial next-nearest-neighbour Ising (ANNNI) model with higher-order spin interaction." Journal of Physics A: Mathematical and General 27, no. 8 (April 21, 1994): 2675–86. http://dx.doi.org/10.1088/0305-4470/27/8/007.

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11

Zhang, Jing, and Pavel A. Korzhavyi. "First Principles Investigation on Thermodynamic Properties and Stacking Fault Energy of Paramagnetic Nickel at High Temperatures." Metals 10, no. 3 (February 28, 2020): 319. http://dx.doi.org/10.3390/met10030319.

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Reliable data on the temperature dependence of thermodynamic properties of alloy phases are very useful for modeling the behavior of high-temperature materials such as nickel-based superalloys. Moreover, for predicting the mechanical properties of such alloys, additional information on the energy of lattice defects (e.g., stacking faults) at high temperatures is highly desirable, but difficult to obtain experimentally. In this study, we use first-principles calculations, in conjunction with a quasi-harmonic Debye model, to evaluate the Helmholtz free energy of paramagnetic nickel as a function of temperature and volume, taking into account the electronic, magnetic, and vibrational contributions. The thermodynamic properties of Ni, such as the equilibrium lattice parameter and elastic moduli, are derived from the free energy in the temperature range from 800 to 1600 K and compared with available experimental data. The derived temperature dependence of the lattice parameter is then used for calculating the energies of intrinsic and extrinsic stacking faults in paramagnetic Ni. The stacking fault energies have been evaluated according to three different methodologies, the axial-next-nearest-neighbor Ising (ANNNI) model, the tilted supercell approach, and the slab supercell approach. The results show that the elastic moduli and stacking fault energies of Ni decrease with increasing temperature. This “softening” effect of temperature on the mechanical properties of nickel is mainly due to thermal expansion, and partly due to magnetic free energy contribution.
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12

Ruffino, Martina, Guy C. G. Skinner, Eleftherios I. Andritsos, and Anthony T. Paxton. "Ising-like models for stacking faults in a free electron metal." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 476, no. 2242 (October 2020): 20200319. http://dx.doi.org/10.1098/rspa.2020.0319.

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We propose an extension of the axial next nearest neighbour Ising (ANNNI) model to a general number of interactions between spins. We apply this to the calculation of stacking fault energies in magnesium—particularly challenging due to the long-ranged screening of the pseudopotential by the free electron gas. We employ both density functional theory (DFT) using highest possible precision, and generalized pseudopotential theory (GPT) in the form of an analytic, long ranged, oscillating pair potential. At the level of first neighbours, the Ising model is reasonably accurate, but higher order terms are required. In fact, our ‘ AN N NI model’ is slow to converge—an inevitable feature of the free electron-like electronic structure. In consequence, the convergence and internal consistency of the AN N NI model is problematic within the most precise implementation of DFT. The GPT shows the convergence and internal consistency of the DFT bandstructure approach with electron temperature, but does not lead to loss of precision. The GPT is as accurate as a full implementation of DFT but carries the additional benefit that damping of the oscillations in the AN N NI model parameters are achieved without entailing error in stacking fault energies. We trace this to the logarithmic singularity of the Lindhard function.
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13

Matsumoto, Takahiro, Atsuo Fukuda, Masahiro Johno, Yuki Motoyama, Tomoyuki Yui, San-Seong Seomun, and Mamoru Yamashita. "A novel property caused by frustration between ferroelectricity and antiferroelectricity and its application to liquid crystal displays-frustoelectricity and V-shaped switching." Journal of Materials Chemistry 9, no. 9 (1999): 2051–80. http://dx.doi.org/10.1039/a903273h.

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We have studied the frustration between ferro- and antiferro-electricity in chiral smectic C like liquid crystalline phases, which is not only fundamentally interesting but also very attractive from an application point of view. It causes temperature induced successive phase transitions as characterized by a devil's staircase and the thresholdless, hysteresis-free, V-shaped switching induced by an applied electric field. The devil's staircase indicates some type of interlayer ordering, while the V-shaped switching suggests considerably diminished tilting correlation. These two are apparently contradictory to each other, but result from the same cause, i.e. the frustration. We have first summarized experimental facts regarding subphases and successive phase transitions observed in many compounds and mixtures, which we believe are related to one another and result from the frustration. We have introduced several different theoretical explanations for these observed facts, and shown that only the axial next nearest neighbor Ising (ANNNI) model can explain almost all of the facts, provided that it is unified with the XY model appropriately. The unified model can make a comprehensive explanation in the most natural way based on the most probable molecular interactions. We have then emphasised that there are several modes regarding the V-shaped switching, because the system becomes so soft with respect to the tilting direction and sense that any additional external or internal force modifies the in-plane local director alignments. For the practically usable ones, we have emphasised the need for some type of randomization in the molecular alignment at the tip of the V and/or the switching process. In particular, the two dimensional (ideally, cylindrically symmetric) azimuthal angle distribution of local in-plane directors around the smectic layer normal is most attractive. Such a randomized state at the tip of the V is thermodynamically unique under a given condition imposed by interfaces. It stays stable even when the smectic layer structure, such as a chevron, changes with temperature. Finally, we have summarized the so-far reported compounds and mixtures for the V-shaped switching and introduced some prototypes of LCDs using them.
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14

Berera, Arjun, and Byungnam Kahng. "Axial next-nearest-neighbor Ising-model roughening transitions." Physical Review E 47, no. 4 (April 1, 1993): 2317–20. http://dx.doi.org/10.1103/physreve.47.2317.

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15

Harris, A. B., C. Micheletti, and J. M. Yeomans. "Quantum Fluctuations in the Axial Next-Nearest-Neighbor Ising Model." Physical Review Letters 74, no. 15 (April 10, 1995): 3045–48. http://dx.doi.org/10.1103/physrevlett.74.3045.

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16

Mo, Z., and M. Ferer. "Three-dimensional axial next-nearest-neighbor Ising model: A series investigation." Physical Review B 43, no. 13 (May 1, 1991): 10890–905. http://dx.doi.org/10.1103/physrevb.43.10890.

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17

Kasama, Toshihiro, Yoshinori Muraoka, and Toshihiro Idogaki. "Partially disordered states of mixed-spin axial next-nearest-neighbor Ising model." Journal of Magnetism and Magnetic Materials 272-276 (May 2004): E1015—E1016. http://dx.doi.org/10.1016/j.jmmm.2003.12.1341.

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18

Hassold, Gregory N., and David J. Srolovitz. "Ordering in the quenched two-dimensional axial next-nearest-neighbor Ising model." Physical Review B 37, no. 7 (March 1, 1988): 3467–79. http://dx.doi.org/10.1103/physrevb.37.3467.

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19

Derian, René, Andrej Gendiar, and Tomotoshi Nishino. "Modulation of Local Magnetization in Two-Dimensional Axial-Next-Nearest-Neighbor Ising Model." Journal of the Physical Society of Japan 75, no. 11 (November 15, 2006): 114001. http://dx.doi.org/10.1143/jpsj.75.114001.

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20

Sato, A., and F. Matsubara. "Equilibrium properties of an axial next-nearest-neighbor Ising model in two dimensions." Physical Review B 60, no. 14 (October 1, 1999): 10316–24. http://dx.doi.org/10.1103/physrevb.60.10316.

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21

Grynberg, Marcelo D., and Horacio Ceva. "Interacting-fermion approximation in the two-dimensional axial next-nearest-neighbor Ising model." Physical Review B 43, no. 16 (June 1, 1991): 13630–33. http://dx.doi.org/10.1103/physrevb.43.13630.

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22

Sen, Diptiman. "Large-Sanalysis of a quantum axial next-nearest-neighbor Ising model in one dimension." Physical Review B 43, no. 7 (March 1, 1991): 5939–43. http://dx.doi.org/10.1103/physrevb.43.5939.

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23

Cheon, Mookyung, and Iksoo Chang. "Anisotropic Domain Growth of the Axial Next-Nearest-Neighbor Ising Model at Low Temperatures." Physical Review Letters 86, no. 20 (May 14, 2001): 4576–79. http://dx.doi.org/10.1103/physrevlett.86.4576.

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24

Kaski, K., and W. Selke. "Monte Carlo coarse graining for the three-dimensional axial next-nearest-neighbor Ising model." Physical Review B 31, no. 5 (March 1, 1985): 3128–30. http://dx.doi.org/10.1103/physrevb.31.3128.

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25

Massidda, Vittorio, and Claudio R. Mirasso. "Axial next-nearest-neighbor Ising model, dipole-dipole interactions, and the phase transitions ofNaNO2." Physical Review B 40, no. 13 (November 1, 1989): 9327–28. http://dx.doi.org/10.1103/physrevb.40.9327.

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26

Matsubara, Fumitaka, Nobuo Suzuki, and Takayuki Shirakura. "Low Temperature Phase of a Dilute Axial-next-nearest-neighbor Ising Model in Two Dimensions." Journal of the Physical Society of Japan 89, no. 12 (December 15, 2020): 124001. http://dx.doi.org/10.7566/jpsj.89.124001.

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27

Fisher, Michael E., and Anthony M. Szpilka. "Domain-wall interactions. II. High-order phases in the axial next-nearest-neighbor Ising model." Physical Review B 36, no. 10 (October 1, 1987): 5343–62. http://dx.doi.org/10.1103/physrevb.36.5343.

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28

Tamashiro, M. N., C. S. O. Yokoi, and S. R. Salinas. "Mean-field calculations for the axial next-nearest-neighbor Ising model in a random field." Physical Review B 56, no. 13 (October 1, 1997): 8204–11. http://dx.doi.org/10.1103/physrevb.56.8204.

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29

Yokoi, Carlos S. O. "Asymmetric phases in the mean-field theory of the axial next-nearest-neighbor Ising model." Physical Review B 43, no. 10 (April 1, 1991): 8487–90. http://dx.doi.org/10.1103/physrevb.43.8487.

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30

D’Elía, Santiago. "Quantum studies of the two-dimensional axial next-nearest-neighbor Ising model: A BCS-type theory." Physical Review B 43, no. 1 (January 1, 1991): 1202–5. http://dx.doi.org/10.1103/physrevb.43.1202.

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31

D’Elía, Santiago. "Hamiltonian limit of the two-dimensional axial next-nearest-neighbor Ising model: A many-body approach." Physical Review B 46, no. 5 (August 1, 1992): 3128–31. http://dx.doi.org/10.1103/physrevb.46.3128.

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32

Grynberg, Marcelo D., and Horacio Ceva. "Finite-size-scaling estimation of critical exponents in the two-dimensional axial next-nearest-neighbor Ising model." Physical Review B 38, no. 13 (November 1, 1988): 9172–77. http://dx.doi.org/10.1103/physrevb.38.9172.

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33

Kasama, Toshihiro, Toshihiro Idogaki, and Yoshinori Muraoka. "Monte Carlo Study of the Partially Disordered States of Mixed-spin Axial Next-nearest-neighbor Ising Model." Czechoslovak Journal of Physics 54, S4 (December 2004): 635–38. http://dx.doi.org/10.1007/s10582-004-0161-9.

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34

Muraoka, Y., H. Nishiyama, T. Kasama, and T. Idogaki. "Non-equilibrium Relaxation in the Three-dimensional Axial Next-nearest-neighbor Ising Model with Alternating Intralayer Interactions." Czechoslovak Journal of Physics 54, S4 (December 2004): 639–42. http://dx.doi.org/10.1007/s10582-004-0162-8.

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35

DeSimone, Tony, Richard M. Stratt, and Jan Tobochnik. "Some developments in the theory of modulated order. II. Deformable-lattice models and the axial next-nearest-neighbor Ising model as a random magnet." Physical Review B 32, no. 3 (August 1, 1985): 1549–57. http://dx.doi.org/10.1103/physrevb.32.1549.

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36

DeSimone, Tony, and Richard M. Stratt. "Some developments in the theory of modulated order. I. The role of fluctuations in the axial next-nearest-neighbor Ising model and the relevance of the Thouless-Anderson-Palmer equation." Physical Review B 32, no. 3 (August 1, 1985): 1537–48. http://dx.doi.org/10.1103/physrevb.32.1537.

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37

Jagodzinski, H. "The role of entropy in polytypism of SiC and ZnS." Zeitschrift für Kristallographie - Crystalline Materials 210, no. 7 (January 1, 1995). http://dx.doi.org/10.1524/zkri.1995.210.7.481.

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AbstractThe ANNNI model (Axial Next-Nearest-Neighbor Ising model), as developed for the explanation of polytypism in magnetic structures, was the first to introduce entropy contributions to free energies of magnetic polytypes. Phonon and other contributions to entropy have recently been included, in order to interpret some of the polytypes of SiC and ZnS as thermodynamically stable structures. It is shown in this paper that polytypism is strongly dependent on crystal size in these cases. Hence disorder has to be included into the discussion of equilibrium conditions. Phonon and vibrational entropy seem to play the predominant role in the ordering process during crystal growth. Consequently, kinetics is also an important factor in interpreting the distribution laws of polytypic structures. The existence of certain branches may be explained with the aid of size degeneracies and size instabilities as defined in this paper.
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38

Fobes, David M., Shi-Zeng Lin, Nirmal J. Ghimire, Eric D. Bauer, Joe D. Thompson, Markus Bleuel, Lisa M. DeBeer-Schmitt, and Marc Janoschek. "Realization of the axial next-nearest-neighbor Ising model in U3Al2Ge3." Physical Review B 96, no. 17 (November 9, 2017). http://dx.doi.org/10.1103/physrevb.96.174413.

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39

Zhang, Kai, and Patrick Charbonneau. "Monte Carlo Study of the Axial Next-Nearest-Neighbor Ising Model." Physical Review Letters 104, no. 19 (May 13, 2010). http://dx.doi.org/10.1103/physrevlett.104.195703.

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40

Gendiar, A., and T. Nishino. "Phase diagram of the three-dimensional axial next-nearest-neighbor Ising model." Physical Review B 71, no. 2 (January 7, 2005). http://dx.doi.org/10.1103/physrevb.71.024404.

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41

Chandra, Anjan Kumar, and Subinay Dasgupta. "Floating phase in the one-dimensional transverse axial next-nearest-neighbor Ising model." Physical Review E 75, no. 2 (February 7, 2007). http://dx.doi.org/10.1103/physreve.75.021105.

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42

Matsubara, Fumitaka, Takayuki Shirakura, and Nobuo Suzuki. "Domain state of the axial next-nearest-neighbor Ising model in two dimensions." Physical Review B 95, no. 17 (May 5, 2017). http://dx.doi.org/10.1103/physrevb.95.174409.

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43

Biswas, Soham, Anjan Kumar Chandra, and Parongama Sen. "Zero-temperature dynamics in the two-dimensional axial next-nearest-neighbor Ising model." Physical Review E 78, no. 4 (October 21, 2008). http://dx.doi.org/10.1103/physreve.78.041119.

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44

Hu, Yi, and Patrick Charbonneau. "Resolving the two-dimensional axial next-nearest-neighbor Ising model using transfer matrices." Physical Review B 103, no. 9 (March 25, 2021). http://dx.doi.org/10.1103/physrevb.103.094441.

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45

Ouisse, T., and D. Chaussende. "Application of an axial next-nearest-neighbor Ising model to the description ofMn+1AXnphases." Physical Review B 85, no. 10 (March 27, 2012). http://dx.doi.org/10.1103/physrevb.85.104110.

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46

Shirahata, Takashi, and Tota Nakamura. "Infinitesimal incommensurate stripe phase in an axial next-nearest-neighbor Ising model in two dimensions." Physical Review B 65, no. 2 (December 6, 2001). http://dx.doi.org/10.1103/physrevb.65.024402.

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47

Shirakura, T., F. Matsubara, and N. Suzuki. "Kosterlitz-Thouless phase transition of the axial next-nearest-neighbor Ising model in two dimensions." Physical Review B 90, no. 14 (October 8, 2014). http://dx.doi.org/10.1103/physrevb.90.144410.

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48

Dalmazi, D., and F. L. Sá. "Unusual Yang-Lee edge singularity in the one-dimensional axial-next-to-nearest-neighbor Ising model." Physical Review E 82, no. 5 (November 5, 2010). http://dx.doi.org/10.1103/physreve.82.051108.

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49

Kasama, T., Y. Muraoka, and T. Idogaki. "Molecular field and Monte Carlo study for the mixed-spin axial next-nearest-neighbor Ising model." Physical Review B 73, no. 21 (June 7, 2006). http://dx.doi.org/10.1103/physrevb.73.214411.

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50

Muraoka, Y., T. Kasama, T. Shimamoto, K. Okada, and T. Idogaki. "Partially disordered phases in the three-dimensional axial next-nearest-neighbor Ising model with alternating intralayer interactions." Physical Review B 66, no. 6 (August 20, 2002). http://dx.doi.org/10.1103/physrevb.66.064427.

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