Approximate method of free energy calculation for spin system with arbitrary connection matrix

TL;DR

This paper introduces an approximate method for calculating free energy in spin systems with arbitrary connection matrices, leveraging Gaussian approximation of energy distribution, effective for both long-range and short-range interactions.

Contribution

It presents a novel Gaussian-based approximation method for free energy calculation applicable to diverse spin systems with arbitrary connections.

Findings

Effective for systems with large coordination number q

Provides good results for short-range interactions with smaller q

Applicable to systems with arbitrary connection matrices

Abstract

The proposed method of the free energy calculation is based on the approximation of the energy distribution in the microcanonical ensemble by the Gaussian distribution. We hope that our approach will be effective for the systems with long-range interaction, where large coordination number q ensures the correctness of the central limit theorem application. However, the method provides good results also for systems with short-range interaction when the number q is not so large.