Alternative proof of existence of Gibbs measure at high temperature

Abstract

Mathematical models in equilibrium statistical mechanics describe physical systems with many particles interacting with an external force and with one another. Gibbs measure is a fundamental concept in this theory. In existing literature infinite-volume models are constructed as limits of finite models and existence of Gibbs measure for them is proven through DLR formalism. The general existence proofs are quite complicated and involve topology and cluster expansion. In this paper we develop a more transparent and more constructive proof of existence of infinite Gibbs measure for a particular case of interaction model at high temperature. The proof is based on a limiting procedure and involves estimates of series of semi-invariants and graph-related estimates.