Statistical mechanics approach to lattice field theory

TL;DR

This paper explores the use of the mean spherical approximation (MSA), a statistical physics method, to analyze lattice quantum field theories, especially for locating critical lines in complex bosonic models.

Contribution

It demonstrates how MSA can be applied to lattice quantum field theories, extending its use beyond traditional statistical physics models.

Findings

MSA effectively locates critical lines in multi-component bosonic models.

MSA can handle models without positive definite measures, challenging for Monte Carlo methods.

The approach offers a computationally inexpensive alternative for complex lattice theories.

Abstract

The mean spherical approximation (MSA) is a closure relation for pair correlation functions (two-point functions) in statistical physics. It can be applied to a wide range of systems, is computationally fairly inexpensive, and when properly applied and interpreted lead to rather good results. In this paper we promote its applicability to euclidean quantum field theories formulated on a lattice, by demonstrating how it can be used to locate the critical lines of a class of multi-component bosonic models. The MSA has the potential to handle models lacking a positive definite integration measure, which therefore are difficult to investigate by Monte-Carlo simulations.