Loop expansion around the Bethe-Peierls approximation for lattice models

TL;DR

This paper introduces an effective field theory for lattice models that systematically refines the Bethe-Peierls approximation by including loop corrections, improving the accuracy of magnetization and correlation predictions.

Contribution

It develops a systematic method to incorporate loop corrections around the Bethe-Peierls approximation for lattice models, capturing lattice topology exactly.

Findings

Lowest loop corrections improve magnetization estimates.

Correlation functions are refined with systematic loop corrections.

The approach reproduces lattice topology through diagrammatic expansion.

Abstract

We develop an effective field theory for lattice models, in which the only non-vanishing diagrams exactly reproduce the topology of the lattice. The Bethe-Peierls approximation appears naturally as the saddle point approximation. The corrections to the saddle-point result can be obtained systematically. We calculate the lowest loop corrections for magnetisation and correlation function.