Far Eastern Mathematical Journal

To content of the issue

Methods of canonical and multicanonical sempling of phase space of vector models

Shapovalova K.V., Kapitan V.Yu, Makarov A.G, Shevchenko Yu.A., Nefedev K.V.

2017, issue 1, Ñ. 124-130

Methods for numerical calculations of the thermodynamic properties of vector models were presented in the paper. The most popular because of the speed and simplicity of the implementation of canonical sampling is the Metropolis algorithm. Methods of multi-canonical simulation: parallel tempering, also known as replica exchange MC and the Wang-Landau method allow to overcome the shortcomings of the method of canonical modeling.

Metropolis algorithm, Wang-Landau method, parallel tempering

Download the article (PDF-file)


[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] D.P. Landau, K. Binder, A guide to Monte Carlo simulations in statistical physics, Cambridge Univ. Press, 2000, 384 pp.
[3] R. Swendsen and J. Wang, “Replica Monte Carlo Simulation of Spin-Glasses”, Physical review letters, 57:21, (1986), 2607.
[4] C.J. Geyer, “Markov chain Monte Carlo maximum likelihood”, Interface Foundation of North America, 1991.
[5] D.J. Earl and M.W. Deem, “Parallel tempering: Theory, applications, and new perspectives”, Physical Chemistry Chemical Physics, 7, (2005), 3910.
[6] F. Wang and D.P. Landau, “Efficient, multiple-range random walk algorithm to calculate the density of states”, Physical review letters, 86:10, (2001), 2050.
[7] T. Vogel, Y.W. Li, T. Wust, D.P. Landau, “Generic, hierarchical framework for massively parallel Wang-Landau sampling”, Physical review letters, 110:21, (2013), 210603.
[8] T. Vogel, Y.W. Li, T. Wust and D.P. Landau, “Scalable replica-exchange framework for Wang-Landau sampling”, Physical Review E, 90:2, (2014), 023302.
[9] L. Shchur, “Wang-Landau algorithm: random walking on the energy spectrum”, Computational technologies in the natural sciences: methods of supercomputer modeling, ed. R.R. Nazirova, L.N. Shchura, M.: IKI RAS, 2014, 160–166.

To content of the issue