Strong Spatial Mixing for Binary Markov Random Fields

TL;DR

This paper proves strong spatial mixing for binary Markov random fields on sparse graphs when the external field is uniformly large or small, providing insights relevant to physics applications.

Contribution

It establishes conditions for strong spatial mixing in binary Markov random fields based on the magnitude of the external field, a novel theoretical result.

Findings

Proves strong spatial mixing under large or small external field conditions

Applicable to sparse average graphs in physics models

Provides theoretical foundation for phase transition analysis

Abstract

Gibbs distribution of binary Markov random fields on a sparse on average graph is considered in this paper. The strong spatial mixing is proved under the condition that the `external field' is uniformly large or small. Such condition on `external field' is meaningful in physics.