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Journal of Physics C Solid State Physics

Low-temperature expansions for the Ising model with pure triplet interactions on the triangular lattice

M F Sykes, M G Watts, J. L. Martin

Published Dec 11, 1973• 3 citations
Publisher

Abstract

Recently published series expansions of Griffiths and Wood (1973) for the Ising model with pure triplet interactions on the triangular lattice are found to be inconsistent with the exact solution of Baxter and Wu (1973). The necessary corrections are given.
DOI
10.1088/0022-3719/6/24/003

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Journal of Physics A Mathematical and General•Mar 1, 1976•5 citations
For pt. II, see abstr. A64455 of 1973. The critical-point exponents of two Ising models with pure three-spin coupling terms are examined using low-temperature (T<T c ) series expansions for the thermodynamic functions. In particular the critical isotherm exponent delta is examined by applying numerical extrapolation methods to the critical isotherm. The two models are (a) a two-dimensional triangular lattice and (b) a three-dimensional face-centred cubic lattice. Direct numerical estimates of alpha ', beta and delta for (b) show that the scaling relations hold for this model and it is found that alpha '=0.655, beta =0.0538, gamma =1.24, nu =0.448, eta =-0.76, and delta =24 on the basis of the scaling relations. The numerical accuracy of the exponents beta and delta for model (a) does not permit an independent verification of the scaling relations; assuming scaling to hold here also, and using the exact result alpha '= 2 / 3 obtained by Baxter and Wu, it is found that gamma '=1.187+or-0.006, nu = 2 / 3 , eta =0.219+or-0.009, beta =0.073+or-0.003, and delta =17.3+or-0.8.