Low-temperature expansions for Ising models with pair, triplet and quartet interactions present. II

Abstract

Low-temperature perturbation expansions are developed for Ising model lattice assemblies for which in addition to the conventional pair interactions systems of triplets and quartets of spins are coupled in terms of nearest-neighbour linkages. The two models discussed are (i) the triangular lattice with pair interactions between nearest-neighbour sites and triplet interactions over the elementary mesh cycles of the lattice, and (ii) the face centred cubic lattice with nearest-neighbour pair interactions and triplet and quartet coupling defined over the elementary triangles and tetrahedra of the lattice. These multiplets of coupled spins form the simplex subgraphs of the underlying lattice structure which enables the simplex transformations relating the low temperature and high temperature developments of the Ising model problem to be used in obtaining low-temperature power series for the partition function and related thermodynamic functions.