Correlated cluster mean-field theory for spin systems

TL;DR

This paper introduces a correlated cluster mean-field theory for spin systems, improving accuracy over standard mean-field methods by incorporating inter-cluster correlations, and demonstrates its effectiveness on Ising and Heisenberg models.

Contribution

A novel cluster mean-field approach that accounts for correlations between clusters, providing more accurate results for spin models.

Findings

Critical temperature predictions are within 5% of exact values.

Method accurately captures qualitative and quantitative behaviors of spin models.

Effective for different lattice geometries like honeycomb and square lattices.

Abstract

A cluster mean-field method is introduced and the applications to the Ising and Heisenberg models are demonstrated. We divide the lattice sites into clusters whose size and shape are selected so that the equivalence of all sites in a cluster is preserved. Since the strength of interactions of a cluster with its surrounding clusters is strongly dependent on the spin configuration of the central cluster itself, we include this contribution in the effective fields acting on the spins. The effects of "correlations" between clusters can be taken into account beyond the standard mean-field level, and as a result our cluster-based method gives qualitatively (and even quantitatively) correct results for the both Ising and Heisenberg models. Especially, for the Ising model on the honeycomb and square lattices, the calculated results of the critical temperature are very close (overestimated by only less than 5 %) to the exact values.