Gibbs Fields: Uniqueness and Decay of Correlations. Revisiting Dobrushin and Pechersky

TL;DR

This paper refines the proof of the Dobrushin-Pechersky uniqueness criterion for Gibbs fields on general graphs, establishing conditions for uniqueness and exponential decay of correlations even in non-locally compact spaces.

Contribution

It provides a detailed, extended proof of the uniqueness criterion applicable to broader classes of Gibbs fields, including non-locally compact spaces.

Findings

Extended the Dobrushin-Pechersky criterion to general graphs and non-locally compact spaces

Proved exponential decay of correlations under the uniqueness condition

Enhanced understanding of Gibbs fields in complex graph structures

Abstract

We give a detailed and refined proof of the Dobrushin-Pechersky uniqueness criterion extended to the case of Gibbs fields on general graphs and single-spin spaces, which in particular need not be locally compact. The exponential decay of correlations under the uniqueness condition has also been established.