Detecting Classical Phase Transitions with Renyi Mutual Information

TL;DR

This paper introduces a new Monte Carlo method to compute Renyi Mutual Information in classical systems, effectively detecting phase transitions and their universality classes, including topological ones, without relying on traditional order parameters.

Contribution

We develop a replica-trick based approach to calculate Renyi Mutual Information in classical models, enabling detection of various phase transitions and their universality classes.

Findings

Renyi Mutual Information detects finite-temperature critical points.

It can identify the universality class of phase transitions.

It successfully detects topological vortex-unbinding transitions.

Abstract

By developing a method to represent the Renyi entropies via a replica-trick on classical statistical mechanical systems, we introduce a procedure to calculate the Renyi Mutual Information in any Monte Carlo simulation. Through simulations on several classical models, we demonstrate that the Renyi Mutual Information can detect finite-temperature critical points, and even identify their universality class, without knowledge of an order parameter or other thermodynamic estimators. Remarkably, in addition to critical points mediated by symmetry breaking, the Renyi Mutual Information is able to detect topological vortex-unbinding transitions, as we explicitly demonstrate on simulations of the XY model.