Cluster expansions for the Ising and Heisenberg spin models in Hamiltonian lattice field theory

Abstract

Cluster expansion methods are applied to calculate 'high-temperature' series for the vacuum energy, the susceptibility and the mass gap for the Ising model and the O(2) and O(3) Heisenberg models in (1+1) dimensions and (2+1) dimensions. Critical points and critical indices are estimated for the line, the square and the triangular lattices. The results demonstrate universality with the normal Euclidean versions of these models, within errors.