The Three Body Ising Model at Low Temperature

Abstract

Pirogov-Sinai theory is a highly technical and complicated set of procedures which can be used give rigorous proofs for many models which satisfy a gen eral set of constraints. This work was originally set out to be a proof, using Pirogov-Sinai theory, about the phase of a perturbed Ising Model which lacked symmetry. Pirogov-Sinai theory is excellent for such models and is one of the few systematic ways to approach it. The generalization of such a proof how ever, has already been done [5]. Thus, this works concentrates primarily on the background needed to understand Pirogov-Sinai theory, as well as serve as compact and elementary introduction to rigorous statistical mechanics in general. Care was taken to limit the assumptions needed in the proofs to a minimum.