Journal of Physics A Mathematical and General

Exact decimation transformation with mean-field approximation

Kun-Fa Tang, Jia-Zhen Hu

Published Jul 11, 1986• 2 citations

Abstract

A new method is developed for calculating the critical temperature and exponents of spin systems, based on the exact decimation transformation and a mean-field approximation. Calculations of both exponents and critical couplings are much improved, even in the lowest approximation, when compared with other renormalisation group methods.

DOI: 10.1088/0305-4470/19/10/012

Related papers

Two-step renormalisation group for Ising systems

O. F. de Alcantara Bonfim, F. C. Sá Barreto, M. A. De Moura

A decimation transformation preceded by a mean-field renormalisation group has been used to obtain the critical properties of various d-dimensional lattices. The method improves substantially both exponents and critical couplings even for small size clusters when compared with decimation and mean-field renormalisation group methods.

Journal of Physics C Solid State PhysicsAug 20, 19849 citations

Exact Decimation Approach with Mean-Field Approximation for Randomly Diluted Ising Models

TANG KUN-FA, HU JIA-ZHEN

A new renormalization approach developed by authors previously is generalized to disordered systems. Calculations of the critical temperature, concentration, exponents, and of limiting slope of critical curve for the random bond-diluted Ising model on the square lattice, even in the lowest approximation, are in very satisfactory agreement with all known exact or series results.

Communications in Theoretical PhysicsJun 1, 19880 citations

A renormalisation-group method for lattice gas models

A. Šurda

A new method for calculating the critical temperature and critical exponents of classical discrete models, based on the renormalisation-group method and the cluster variational method, is developed. In the lowest approximation, using the mean field approximation and quasichemical approximation, the results for the two-dimensional Ising model are obtained within 2% accuracy.

Journal of Physics A Mathematical and GeneralSep 11, 19843 citations

APPLICATION OF AN EXACT DECIMATION TRANSFORMATION WITH MEAN-FIELD APPROXIMATION METHOD TO THE POTTS MODEL

Ang K

In this paper, the critical exponents of the Potts model are calculated by using the exact decimation with mean-field approximation method~[8]. The results obtained are in good agreement with that of the exact calculation. The accurary of this method is better than other renor-malisation group methods.

Acta Physica SinicaJan 1, 19870 citations

APPLICATION OF AN EXACTDECIMATION TRANSFORMATION WITH MEAN一FIELD APPROXIMATION METHOD TO THE POTTS MODEL

Ye Qing，Tang Kun-fa，Hu Jia-zhen

摘要本文运用作者所发展的严格docimation- 平均场近似方法对Potts 模型的临界指数作了计算.所得结果与严格解符合得很好, 而与计算工作量相当的重正化群方法相比, 精确度大为提高。 Abstract In this paper, the critical exponents of the Potts model are calculated by using the exact decimation with mean-field approximation method. The results obtained are in good agreement with that of the exact calculation. The accurary of this method is better than other renormalization group methods. 作者及机构信息叶青；唐坤发；胡嘉校 1. 上海交通大学应用物理系,；凝聚态物理研究所 Authors and contacts Ye Qing;Tang Kun-fa; Hu Jia-zhen 参考文献施引文献

Acta Physica SinicaJan 1, 19870 citations

Decimation transformations for two-dimensional Ising spin systems

Leigh Sneddon, Michael N. Barber

The decimation transformation is used to calculate critical exponents for two-dimensional Ising spin systems on the square, triangular and hexagonal lattices. Both cumulant and cluster approximations are used. While the results of the low-order cumulant and of small cluster calculations agree well with the known exact exponents, an increase in cluster size does not appear to increase accuracy. The decimation transformation is only found to be useful for calculating thermal eigenvalues.

Journal of Physics C Solid State PhysicsJul 28, 197711 citations