Mean distribution approach to spin and gauge theories

TL;DR

This paper introduces a mean distribution approach that self-consistently determines all moments of link and plaquette distributions in spin and gauge theories, improving upon traditional mean-field approximations.

Contribution

It develops a novel self-consistent framework for distributions in spin and gauge models, extending beyond first-moment approximations.

Findings

Enhanced accuracy over traditional mean-field methods

Applicable to both Abelian and non-Abelian theories

Provides a systematic way to determine all moments of distributions

Abstract

We formulate self-consistency equations for the distribution of links in spin models and of plaquettes in gauge theories. This improves upon known mean-field, mean-link, and mean-plaquette approximations in such that we self-consistently determine all moments of the considered variable instead of just the first. We give examples in both Abelian and non-Abelian cases.