Alternative proof of existence of Gibbs measure at high temperature

TL;DR

This paper presents a new, more transparent proof for the existence of Gibbs measures in high-temperature models, simplifying previous complex methods by using a limiting procedure and series estimates.

Contribution

It introduces a constructive proof for Gibbs measure existence at high temperature, avoiding complex topology and cluster expansion techniques used previously.

Findings

Proof is more transparent and constructive.

Validates Gibbs measure existence for high-temperature models.

Uses series of semi-invariants and graph estimates.

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.