Конечно-размерный скейлинг в ферромагнитных спиновых системах на решетке пирохлора |
К.С. Солдатов, М.А. Падалко, В.C. Стронгин, Д.Ю. Капитан, Е.В. Васильев, А.Е. Рыбин, В.Ю. Капитан, К.В. Нефедев |
2020, выпуск 2, С. 255–266 DOI: https://doi.org/10.47910/FEMJ202026 |
Аннотация |
В работе представлены результаты высокопроизводительных вычислений модели Изинга, XY-модели и классической модели Гейзенберга для решетки пирохлора. Расчеты осуществлялись с помощью алгоритмов Вольффа и Свендсена – Ванга в GPU-реализации. С использование метода конечно-размерного скейлинга были вычислены критические индексы и критические температуры. |
Ключевые слова: Монте-Карло моделирование, конечно-размерный скейлинг, модель Изинга, модель Гейзенберга, классическая XY-модель, решетка пирохлора |
Полный текст статьи (файл PDF) |
Библиографический список |
[1] H. E. Stanley, Introduction to Phase Transitions and Critical Phenomena, Oxford Univ. Press, New York, 1971. [2] C.-K. Hu, “Historical Review on Analytic, Monte Carlo, and Renormalization Group Ap- proaches to Critical Phenomena of Some Lattice Models”, Chinese J. Phys., 52:1, (2014), 1–76. [3] M. J. Harris, S. T. Bramwell, D. F. McMorrow, T. Zeiske, K. W. Godfrey, “Geometrical Frustration in the Ferromagnetic Pyrochlore Ho2T i2O7”, Phys. Rev. Lett., 79:13, (1997). [4] A. P. Ramirez, A. Hayashi, R. J. Cava, R. Siddharthan, B. S. Shastry, “Zero-point entropy inspinice”, Nature (London), 399, (1999), 333–335. [5] S. T. Bramwell, J. P. Gingras, “Spin Ice State in Frustrated Magnetic Pyrochlore Materials”, Science, 294:5546, (2001), 1495–1501. [6] X. Ke, R. S. Freitas, B. G. Ueland, G. C. Lau, M. L. Dahlberg, R. J. Cava, R. Moessner, P. Schiffer, “Nonmonotonic Zero-Point Entropy in Diluted Spin Ice”, Phys. Rev. Lett., 99, (2007), 137203. [7] Y. Shevchenko, K. Nefedev, Y. Okabe, “Entropy of diluted antiferromagnetic Ising models on frustrated lattices using the Wang-Landau method”, Physical Review E, 95:5, (2017), 052132. [8] D. P. Landau, K. Binder, A Guide to Monte Carlo Simulations in Statistical Physics, 3rd edition, Cambridge University Press, Cambridge, 2009. [9] N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, E. Teller, “Equation of State Calculations by Fast Computing Machines”, J. Chem. Phys., 21:6, (1953), 1087. [10] R. H. Swendsen, J. S. Wang, “Nonuniversal critical dynamics in Monte Carlo simulations”, Phys. Rev. Lett., 58, (1987), 86. [11] U. Wolff, “Collective Monte Carlo Updating for Spin Systems”, Phys. Rev. Lett., 62, (1989), 361. [12] Y. Komura, Y. Okabe, “GPU-based Swendsen-Wang multi-cluster algorithm for the simulation of two-dimensional classical spin systems”, Comput. Phys. Comm., 183, (2012), 1155. [13] K. A. Hawick, A. Leist, D. P. Playne, “Parallel Graph Component Labelling with GPUs and CUDA”, Parallel Computing, 36, (2010), 655. [14] O. Kalentev, A. Rai, S. Kemnitzb, R. Schneider, “Connected component labeling on a 2D grid using CUDA”, J. Parallel Distrib. Comput., 71, (2011), 615. [15] Y. Komura, “A generalized GPU-based connected component labeling algorithm”, Comput. Phys. Comm., 194, (2015), 54, arXiv: 1603.08357. [16] Y. Komura, Y. Okabe, “CUDA programs for the GPU computing of the Swendsen–Wang multi-cluster spin flip algorithm: 2D and 3D Ising, Potts, and XY models”, Comput. Phys. Comm., 185, (2014), 1038–1043. [17] Y. Komura, Y. Okabe, “Improved CUDA programs for GPU computing of Swendsen–Wang multi-cluster spin flip algorithm: 2D and 3D Ising, Potts, and XY models”, Comput. Phys. Comm., 200, (2016), 400–401. [18] Y. Komura, Y. Okabe, “Large-Scale Monte Carlo Simulation of Two-Dimensional Classical XY Model Using Multiple GPUs”, J. Phys. Soc. Jpn., 81, (2012), 113001. [19] Y. Komura, Y. Okabe, “High-Precision Monte Carlo Simulation of the Ising Models on the Penrose Lattice and the Dual Penrose Lattice”, J. Phys. Soc. Jpn., 85, (2016), 044004. [20] H. Shinaoka, Y. Tomita, Y. Motome, “Effect of magnetoelastic coupling on spin-glass be- havior in Heisenberg pyrochlore antiferromagnets with bond disorder”, Phys. Rev. B, 90, (2014), 165119. [21] J. H. Van Vleck, The Theory of Electric and Magnetic Susceptibilities, Oxford University Press, Oxford University Press, O, 1932. [22] M. E. Fisher, “The Theory of critical point singularities”, Proc. 1970 E. Fermi Int. School of Physics, v. 51, ed. M.S. Green, Academic, New York, 1971, 1–99. [23] K. Binder, “Finite size scaling analysis of ising model block distribution functions”, Z. Phys. B: Condens. Matter, 43, (1981), 119. [24] Л. Д. Ландау, Е. М. Лифшиц, Теоретическая физика, В 10 т. Т. 5 (В 2 ч. Ч.1) Стати- стическая физика, Физматлит, М., 2013. [25] C.-K. Hu, C.-Y. Lin, J.-A. Chen, “Universal Scaling Functions in Critical Phenomena”, Phys. Rev. Lett., 75, (1995), 193. [26] Y. Okabe, M. Kikuchi, “Universal finite-size-scaling functions”, International Journal of Modern Physics C, 7, (1996), 287–294. [27] Y. Okabe, K. Kaneda, M. Kikuchi, C.-K. Hu, “Universal finite-size scaling functions for critical systems with tilted boundary conditions”, Phys. Rev. E, 59, (1999), 1585. [28] Y. Tomita, Y. Okabe, C.-K. Hu, “Cluster analysis and finite-size scaling for Ising spin systems”, Phys. Rev. E, 60, (1999), 2716. [29] M.-C. Wu, C.-K. Hu, N. Sh. Izmailian, “Universal finite-size scaling functions with exact nonuniversal metric factors”, Phys. Rev. E, 67, (2003), 065103(R). [30] H. W. J. Bl?ote, E. Luijten, J. R. Heringa, “Ising universality in three dimensions: a Monte Carlo study”, J. Phys. A: Math. Gen., 28, (1995), 6289. [31] M. Campostrini, M. Hasenbusch, A. Pelissetto, P. Rossi, E. Vicari, “Critical behavior of the three-dimensional XY universality class”, Phys. Rev. B, 63, (2001), 214503. [32] A. P. Gottlob, M. Hasenbusch, S. Meyer, “Critical behaviourof the 3D XY-model: A Monte Carlo study”, Nucl. Phys. B (Proc. Suppl.), 30, (1993), 838. [33] M. Campostrini, M. Hasenbusch, A. Pelissetto, P. Rossi, E. Vicari, “Critical exponents and equation of state of the three-dimensional Heisenberg universality class”, Phys. Rev. B, 65, (2002), 144520. [34] C. Holm, W. Janke, “Critical exponents of the classical three-dimensional Heisenberg model: A single-cluster Monte Carlo study”, Phys. Rev. B, 48, (1993), 936. |