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physica status solidi (b)

Extended chain approximation in quasi‐one‐dimensional ising model

Y. Muraoka, Toshihiro Idogaki

Published Jun 1, 1996• 4 citations
Publisher

Abstract

Abstract The extended chain approximation (ECA) in the quasi‐one‐dimensional Ising model is proposed and is found to give the same results as the Bethe‐Peierls approximation for the ferromagnetic Ising model. It is discussed that the ECA can be applied to complicated systems such as the axial next‐nearest‐neighbour Ising (ANNNI) model, etc.

DOI
10.1002/pssb.2221950224

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Abstract The extended chain approximation (ECA) in the quasi‐one‐dimensional Ising model is proposed and is found to give the same results as the Bethe‐Peierls approximation for the ferromagnetic Ising model. It is discussed that the ECA can be applied to complicated systems such as the axial next‐nearest‐neighbour Ising (ANNNI) model, etc.
We have proposed a cluster heat bath(CHB) method of a quasi-one dimensional Ising model and demonstrated that it reproduces the exact results of the two dimensional Ising model with axially anisotropic exchange interactions. The point of the method is to select one of the equilibrium spin configurations of each of the chains which are subjected by effective fields of surrounding spins. Thus the chains are always in their equilibrium state during the simulation and the ddd dimensional model effectively becomes as a d−1d-1d−1 dimensional model of fictitious spins with their freedom of 2N2^N2N and the simulation time is drastically reduced, where NNN is the number of the spins on the chain.
We study a modified mean-field approximation for the Ising Model in arbitrary dimension. Instead of taking a "central" spin, or a small "drop" of fluctuating spins coupled to the effective field of their nearest neighbors as in the Mean-Field or the Bethe-Peierls-Weiss methods, we take an infinite chain of fluctuating spins coupled to the mean field of the rest of the lattice. This results in a significative improvement of the Mean-Field approximation with a small extra effort.