Information Geometry and Phase Transitions

TL;DR

This paper explores how information geometry, particularly scalar curvature, can reveal phase transitions in statistical mechanics models, with curvature diverging at critical points indicating phase changes.

Contribution

It applies the concept of information geometry to solvable models, demonstrating how scalar curvature signals phase transitions and provides a geometric perspective.

Findings

Scalar curvature R is zero for non-interacting models.

R diverges at critical points of interacting models.

Information geometry offers a geometric interpretation of phase transitions.

Abstract

The introduction of a metric onto the space of parameters in models in Statistical Mechanics and beyond gives an alternative perspective on their phase structure. In such a geometrization, the scalar curvature, R, plays a central role. A non-interacting model has a flat geometry (R=0), while R diverges at the critical point of an interacting one. Here, the information geometry is studied for a number of solvable statistical-mechanical models.