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Prog. Theor. Phys. Vol. 78 No. 3 (1987) pp. 540-551

A Scaling Approach to Monte Carlo Renormalization Group

Macoto Kikuchi and Yutaka Okabe

Department of Physics, Tohoku University, Sendai 980

(Received May 9, 1987)

Abstract:

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 y_H is obtained from the square of block-spin magnetization at the fixed point, while the temperature exponent y_T 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.

URL : http://ptp.ipap.jp/link?PTP/78/540/
DOI : 10.1143/PTP.78.540

[ Full Text PDF : FREE ACCESS (622K) ] Citation: Plain Text BiBTeX EndNote(RIS) RSS

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Citing Article(s) :

1. Journal of the Physical Society of Japan 57 (1988) pp. 16-19 :

   Monte Carlo Simulation of the Ising Model on the Penrose Lattice

   Yutaka Okabe and Komajiro Niizeki

2. Journal of the Physical Society of Japan 60 (1991) pp. 1523-1532 :

   Determination of the Critical Points of Antiferromagnetic Ising Model with Next Nearest Neighbour Interactions on the Triangular Lattice

   Seiji Miyashita, Hidetsugu Kitatani and Yasumasa Kanada

3. Journal of the Physical Society of Japan 66 (1997) pp. 3411-3420 :

   Nature of the Ordered Phase and the Critical Properties of the Three Dimensional Six-State Clock Model

   Seiji Miyashita

4. Journal of the Physical Society of Japan 67 (1998) pp. 816-824 :

   Critical Exponents of Ising-Like Heisenberg Antiferromagnets on the Hexagonal Lattice

   Seizo Watarai and Seiji Miyashita

5. Journal of the Physical Society of Japan 69 (2000) pp. 2250-2260 :

   Phase Diagram of Ising-Like Heisenberg Model on the Triangular Lattice with Degenerate Orbital Effect

   Takuya Arimori and Seiji Miyashita

6. Progress of Theoretical Physics Supplement No.101 (1990) pp. 557-566 :

   Block-Spin Distribution Functions at Criticality

   Macoto Kikuchi

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