Information Geometry for Husimi-Temperley Model

TL;DR

This paper uses information geometry, specifically the Fisher metric, to analyze phase transitions in the Husimi-Temperley model, revealing hyperbolic geometry at critical points and scale invariance.

Contribution

It introduces a geometric approach to phase transitions in the Husimi-Temperley model using the Fisher metric derived from the density matrix.

Findings

The Fisher metric becomes hyperbolic at the critical point.

The metric remains invariant under scale transformations.

Geometric quantities detect phase transitions clearly.

Abstract

We examine phase transition of the Husimi-Temperley model in terms of information geometry. For this purpose, we introduce the Fisher metric defined by the density matrix of the model. We find that the metric becomes hyperbolic at the critical point with respect to the energy scale. Then, the metric is invariant under the scale transformation. We also find that the equation of states is naturally derived from a necessary condition for the entropy operator that is a building block of the metric. Based on these findings, we conclude that the geometric quantities clearly detect the phase transition of the model.