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Progress of Theoretical Physics

A Simple Method of Monte Carlo Renormalization Group

Macoto Kikuchi, Yutaka Okabe

Published Jan 1, 1986• 16 citations
Publisher

Abstract

We propose a simple method of Monte Carlo renormalization group which is based on the transformation properties of the thermodynamic quantities under the block-spin transformation. We apply the method to the three-dimensional Ising model.
DOI
10.1143/ptp.75.192

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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.
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