Cluster Entanglement Mean Field inspired approach to Criticality in Classical Systems

TL;DR

This paper introduces a cluster entanglement mean field approach for classical many-body systems, improving predictions of critical points over traditional mean field theories by incorporating two-body correlations.

Contribution

The authors develop a cluster entanglement mean field theory that considers two-body correlations, enhancing the accuracy of criticality predictions in classical lattice models.

Findings

Better prediction of critical points in Ising models

Improved accuracy over traditional mean field theory

Applicable to various lattice geometries and dimensions

Abstract

We propose an entanglement mean field theory inspired approach for dealing with interacting classical many-body systems. It involves a coarse-graining technique that terminates a step before the mean field theory: While mean field theory deals with only single-body physical parameters, the entanglement mean field theory deals with single- as well as two-body ones. We improve the theory to a cluster entanglement mean field, that deals with a fundamental unit of the lattice of the many-body system. We apply these methods to interacting Ising spin systems in several lattice geometries and dimensions, and show that the predictions of the onset of criticality of these models are much better in the proposed theories as compared to the corresponding ones in mean field theories.