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Journal of Anhui Normal University

The Analysis of Different Size Group Influence on the Renormalization Group in Ising Model

MA Xian-guang

Published Jan 1, 2006• 0 citations
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Abstract

Based on the two dimension triangle crystal lattice spin model,we selected groups which contain seven and nine crystal lattices pins as Kadanoff group.The critical point and exponents results which gained by renormalization group transform indicated that Bigger group can increase the precision.

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Journal of Hubei University•Jan 1, 2005•0 citations
The renormalisation group method of Kadanoff is applied to the spin- 1 / 2 Ising model in two dimensions using a transformation applicable to both the square and triangular lattices. Two types of cluster are studied for the triangular lattice.The first cluster yields a new fixed point but the results for the critical temperature and critical exponents are in poor agreement with the known exact values. The second cluster maps directly onto the fixed point found by Kadanoff for the square lattice yielding excellent values for both the critical exponents and the critical temperature.
The Niemeijer-Van Leeuwen cumulant expansion is used in the renormalization-group analysis of the critical-point behavior of the Ising model. Second- and third-order results are obtained for the simple cubic and square lattices, respectively, for a variety of cell sizes, using a parameter-dependent renormalization transformation introduced by Kadanoff and Houghton. Although the results in two dimensions are in general good, there is no evidence of any convergence, with the best values for the critical exponents and critical temperature being given by the second-order theory. In three dimensions the values found for the critical temperature and magnetic scaling index for a cell of 27 spins are reasonable, but the corresponding thermal scaling index is quite poor.