Mutual information in classical spin models

TL;DR

This paper investigates the behavior of total correlations in classical spin models at finite temperatures using mutual information, revealing that correlations peak in the high-temperature phase rather than at the phase transition.

Contribution

It introduces a numerical approach combining matrix product states and Monte Carlo methods to compute mutual information in classical spin models.

Findings

Mutual information peaks in the paramagnetic phase at high temperatures.

Total correlations are not maximal at the phase transition, contrasting quantum systems.

Numerical methods effectively compute mutual information in 2D Ising and Potts models.

Abstract

The total many-body correlations present in finite temperature classical spin systems are studied using the concept of mutual information. As opposed to zero-temperature quantum phase transitions, the total correlations are not maximal at the phase transition, but reach a maximum in the high temperature paramagnetic phase. The Shannon and Renyi mutual information in both Ising and Potts models in 2 dimensions are calculated numerically by combining matrix product states algorithms and Monte Carlo sampling techniques.