Geodesics in Information Geometry : Classical and Quantum Phase Transitions

TL;DR

This paper investigates the behavior of geodesics on the parameter manifold in classical and quantum systems undergoing second order phase transitions, revealing phase confinement and critical point behavior through numerical solutions.

Contribution

It demonstrates that geodesics are confined within a single phase and show turning points near criticality across diverse models, indicating geometric universality.

Findings

Geodesics are confined to a single phase in both classical and quantum systems.

Geodesics exhibit turning behavior near critical points.

Results suggest a universal geometric structure in phase transitions.

Abstract

We study geodesics on the parameter manifold, for systems exhibiting second order classical and quantum phase transitions. The coupled non-linear geodesic equations are solved numerically for a variety of models which show such phase transitions, in the thermodynamic limit. It is established that both in the classical as well as in the quantum case, geodesics are confined to a single phase, and exhibit turning behavior near critical points. Our results are indicative of a geometric universality in widely different physical systems.