Upper bound on the decay of correlations in a general class of O(N)-symmetric models

TL;DR

This paper establishes algebraic upper bounds on the decay of spin-spin correlations in a broad class of two-dimensional $O(N)$-symmetric models, including long-range interactions, and also provides estimates on resistor network effective resistance.

Contribution

It introduces a general framework for bounding correlations in $O(N)$ models with non-smooth and long-range interactions, extending previous results to more complex systems.

Findings

Algebraic decay bounds for correlations in $O(N)$ models.

Effective resistance estimates for long-range resistor networks.

Applicability to models with non-smooth interactions.

Abstract

We consider a general class of two-dimensional spin systems, with continuous but not necessarily smooth, possibly long-range, $O(N)$-symmetric interactions, for which we establish algebraically decaying upper bounds on spin-spin correlations under all infinite-volume Gibbs measures. As a by-product, we also obtain estimates on the effective resistance of a (possibly long-range) resistor network in which randomly selected edges are shorted.