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The Phase Transition in Z(N) Potts Spin Model: An Analytical Analysis

Young-Suk Song, Iu W

Published Jan 1, 1992• 0 citations
OpenAlex

Abstract

We study the phase transition in Z(N) Pots spin model by an analytical approach—the generalized cumulant expansion with mean field approximation. As a test, we perform the expansion to the third order correction for Z(3), Z(4), Z(5) and Z(6) cases. The critical points turn out to be closer to the exact values when higher order corrections are taken into account.

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Communications in Theoretical Physics•Jun 1, 1992•0 citations
We study the phase transition in Z(N) Pots spin model by an analytical approach—the generalized cumulant expansion with mean field approximation. As a test, we perform the expansion to the third order correction for Z(3), Z(4), Z(5) and Z(6) cases. The critical points turn out to be closer to the exact values when higher order corrections are taken into account.
We investigate the phase transition of the three-state Potts model in an analytical approach—the generalized cumulant expansion with the effective mean field hypothesis. We find a first order phase transition in the three-dimensional three-state Potts model with ferromagnetic nearest neighbor coupling. For the model with antiferromagnetic next-to-nearest neighbor coupling, we find a first order transition when the relative strength of the -coupling is fixed to . The critical values given by this method are also in agreement with the recent high statistics Monte Carlo results.
An effective mean-field theory based on cumulant expansion is expanded to deal with the first-order transition of the Potts model on general d-dimensional hypercubic lattice in this paper. It is a generalized mean-field method developed from the cumulant expansion of average free energy. As we shall see, it gives the traditional mean-field result at its first-order approximation and the effective mean field introduced by this method will be amended with the approximation's order increasing. For a full view of this method, we have carried out calculations up to the seventh-order approximation on a square (d=2)(d=2)(d=2) lattice since some known exact quantites of this case are terminals that should be approached. The results show this method has the potential to be a useful tool to calculate thermodynamical observables of spin systems.