Multispin Monte Carlo Method |

Makarova K.V., Makarov A.G., Padalko M.A., Strongin V.S., Nefedev K.V. |

2020, issue 2, Ñ. 212–220DOI: https://doi.org/10.47910/FEMJ202020 |

Abstract |

The article offers a Monte Carlo cluster method for numerically calculating a statistical sample of the state space of vector models. The statistical equivalence of subsystems in the Ising model and quasi-Markov random walks can be used to increase the efficiency of the algorithm for calculating thermodynamic means. The cluster multispin approach extends the computational capabilities of the Metropolis algorithm and allows one to find configurations of the ground and low-energy states. |

hybrid algorithm, multispin method, ground state, spin systemsKeywords: |

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## References |

[1] N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, E. Teller, “Equation of state calculations by fast computing machines”, The journal of chemical physics, 21:6, (1953), 1087–1092. [2] F. Barakona, “On the computational complexity of Ising spin glass models”, Journal of Physics A: Mathematical and General, 15:10, (1982), 3241. [3] R. H. Swendsen, J. Wang, “Replica Monte Carlo simulation of spin-glasses”, Physical review letters, 57:21, (1986), 2607. [4] R. H. Swendsen, J. Wang, “Nonuniversal critical dynamics in Monte Carlo simulations”, Physical review letters, 58:2, (1987), 86. [5] F. Wang, D. P. Landau, “E?cient, multiple-range random walk algorithm to calculate the density of states”, Physical review letters, 86:10, (2001), 2050. [6] Yu. A. Shevchenko, A. G. Makarov, P. D. Andriushchenko, K. V. Nefedev, “Multicanonical sampling of the space of states of H(2, n)-vector models”, Journal of Experimental and Theoretical Physics, 124:6, (2017), 982–993. [7] F. Wang, P. D. Landau, “E?cient, Multiple-Range Random Walk Algorithm to Calculate the Density of States”, Phys. Rev. Lett., 86:10, (2001), 2050–2053. [8] E. Bittner, A. Nu?baumer, W. Janke, “Make life simple: Unleash the full power of the parallel tempering algorithm”, Physical review letters, 101:13, (2008), 130603. [9] R. H. Swendsen, J. Wang, “Nonuniversal critical dynamics in Monte Carlo simulations”, Phys. Rev. Lett., 58:2, (1987), 86–88. [10] Y. Tomita, Y. Okabe, “Crossover and self-averaging in the two-dimensional site-diluted Ising model: Application of probability-changing cluster algorithm”, Physical Review E, 64:3, (2001), 036114. [11] K. Hartmann, “Ground-state clusters of two-, three-, and four-dimensional +-J Ising spin glasses”, Phys. Rev. E, 63:1, (2000), 016106. [12] O. Melchert, A. K. Hartmann, “Analysis of the phase transition in the two-dimensional Ising ferromagnet using a Lempel-Ziv string-parsing scheme and black-box data-compression utilities”, Phys. Rev. E, 91:2, (2015), 023306. [13] E. Ferdinand, M. E. Fisher, “Bounded and Inhomogeneous Ising Models. I. Speci?c-Heat Anomaly of a Finite Lattice”, Phys. Rev., 185:2, (1969), 832–846. [14] Lacroix, P. Mendels, and F. Mila, “Introduction to frustrated magnetism: materials, experiments, theory”, Springer Science & Business Media, 164, (2011). [15] Gia-Wei Chern, P. Mellado, and O. Tchernyshyov, “Two-Stage Ordering of Spins in Dipolar Spin Ice on the Kagome Lattice”, Phys. Rev. Lett., 106:20, (2011), 207202. [16] G. Moller and R. Moessner, “Magnetic multipole analysis of kagome and arti?cial spin-ice dipolar arrays”, Phys. Rev. B, 80:14, (2009), 140409. [17] A. Chioar, N. Rougemaille and B. Canals, “Ground-state candidate for the classical dipo- lar kagome Ising antiferromagnet”, Phys. Rev. B, 93:21, (2016), 214410. [18] Petr Andriushchenko, “In?uence of cuto? dipole interaction radius and dilution on phase transition in kagome arti?cial spin ice”, Journal of Magnetism and Magnetic Materials, 476, (2019), 284–288. [19] A. Sorokin, S. V. Makogonov and S. P. Korolev, “The Information Infrastructure for Collective Scienti?c Work in the Far East of Russia”, Scienti?c and Technical Information Processing, 44:4, (2017), 302–304. |