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Physical Review Letters

Histogram Monte Carlo renormalization group method for phase transition models without critical slowing down

Chin‐Kun Hu

Published Nov 9, 1992• 48 citations
Publisher

Abstract

Based on the subgraph expansions for phase transition models, we present a histogram Monte Carlo method to calculate the free energy and other physical quantities for such models as continuous functions of the system parameter. The method does not have any critical slowing down. We then use physical quantities thus obtained in a percolation renormalization group method to calculate critical point, critical exponents, and thermodynamic order parameter. Our method gives quite accurate results and may be applied to many phase transition models.

DOI
10.1103/physrevlett.69.2739

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Comment on ‘‘Histogram Monte Carlo renormalization group method for phase transition models without critical slowing down’’

Jouke R. Heringa, Henk W. J. Blöte

A Comment on the Letter by C.-K. Hu Phys. Rev. Lett. 69, 2739 (1992).Received 1 December 1992DOI:https://doi.org/10.1103/PhysRevLett.70.2044©1993 American Physical Society

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We propose a simple method of Monte Carlo renormalization group. Thermodynamic quantities of the block-spin system are analyzed phenomenologically on the basis of scaling concept. The field exponent yH is obtained from the square of block-spin magnetization at the fixed point, while the temperature exponent yT is obtained as a consequence of nonlinearity of the scaling fields. In order to check the effectiveness of the method, we perform calculation on the three-dimensional Ising model. The critical temperature and the two critical exponents are estimated precisely. Finite-size effect is shown to be weak, whose origin is the regular part of the free energy density. Statistical errors of the ratios of the block-spin quantities are proved to be surprisingly small compared to those of the block-spin quantities themselves.