Decay of correlations and uniqueness of Gibbs lattice systems with non-quadratic interaction

TL;DR

This paper extends classical lattice models with unbounded spins to include non-quadratic polynomial interactions, showing that potential growth rates influence the uniqueness and decay of correlations in Gibbs measures.

Contribution

It introduces a framework for non-quadratic polynomial interactions in lattice models, establishing conditions for uniqueness and correlation decay.

Findings

Unique Gibbs measure under certain potential growth conditions

Fast decay of correlations demonstrated

Extension of classical models to non-quadratic interactions

Abstract

We aim this paper to develop the classical lattice models with unbounded spin to the case of non-quadratic polynomial interaction. We demonstrate that the distinct relation between the growths of potentials leads to the uniqueness and the fast decay of correlations for Gibbs measure.