A self dual relation for an Ising model with triplet interactions

Abstract

An Ising model is defined on a simple quadratic lattice which has the usual nearest neighbour pair potential terms (-J2 sigma k sigma l) and also triplet potential terms (-J3 sigma k sigma j sigma l) coupling the spins over the elementary triangular mesh cycles formed by connecting half of the next nearest neighbour sites, such that when J2=0 the model reduces to a triangular lattice with only the triplet potentials present. It is shown that the well known self dual property for the case J2 not=0, J3=0 also holds for the case J2=0, J3 not=0, thereby yielding the likely result that the transition point for both of these cases is given by exp(-2J2,3/kT)= square root 2-1.