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Australian Journal of Physics

Series Analysis of a Three-state Potts Model with Three-site Interactions

Ian Graham Enting

Published Oct 1, 1978• 5 citations
Publisher

Abstract

Series expansions are used to investigate a three-state Potts model which has two-site interactions on the bonds of a triangular lattice and three-site interactions on alternate triangles. Although some of the exponent estimates show variations with interaction strengths, the assumption of scaling constrains the permitted exponent values to such an extent that the possible variations lie within the ranges of uncertainty of individual exponent estimates.

DOI
10.1071/ph780383

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Physical review. B, Condensed matter•Dec 1, 1982•5 citations
Series expansions are used to investigate a three-state Potts model which has two-site interactions on the bonds of a triangular lattice and three-site interactions on alternate triangles. Although some of the exponent estimates show variations with interaction strengths, the assumption of scaling constrains the permitted exponent values to such an extent that the possible variations lie within the ranges of uncertainty of individual exponent estimates.
The qqq-state Potts model on the triangular lattice with both two- and three-spin interactions KKK and LLL (the Schick-Griffiths model) is shown to be equivalent to the qqq-state Potts model on a 3-12 lattice with only two-spin interactions J1{J}_{1}J1​ and J2{J}_{2}J2​. In particular, the J1>0{J}_{1}>0J1​>0 and J2>0{J}_{2}>0J2​>0 model is mapped into a Schick-Griffiths model for a range of the coupling parameters KKK and LLL, so that the two models are in the same universality class. We also show that a recent conjecture by Tsallis on the critical point of the 3-12 model is incorrect.