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Journal of Physics A Mathematical and General

Critical exponents for the four-state Potts model

Ian Graham Enting

Published Apr 1, 1975• 38 citations
Publisher

Abstract

A number of relations are obtained connecting the critical exponents of the Ashkin-Teller model. For the special case of the four-state Potts model these relations predict alpha = 2 / 3 , beta = 1 / 12 , gamma = 7 / 6 , delta =15. Series estimates are in agreement with these predictions.
DOI
10.1088/0305-4470/8/4/001

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A series expansion for the free energy of the q-state Potts model on a square lattice is used to estimate the specific heat critical exponents. The analysis is based on a series transformation which was suggested by the known solution of the two-state Potts (Ising) model, and which makes optimum use of the duality theorem. The transformed series is quite smooth. Neville tables yield the estimates alpha (2)=0.0001+or-0.0003 for the two-state model, alpha (3)=0.296+or-0.002 for the three-state model, and alpha (4)=0.45+or-0.02 for the four-state model. The value for alpha (3) differs considerably from one reported by Straley and Fisher (1973), and substantially improves compliance with the Rushbrooke inequality.