Geometric Critical Exponents in Classical and Quantum Phase Transitions

TL;DR

This paper introduces geometric critical exponents for classical and quantum phase transitions, relating information geometry to critical phenomena, and demonstrates their universality through analytical calculations near curvature singularities.

Contribution

It defines and calculates geometric critical exponents for classical and quantum systems, revealing potential universality across different types of phase transitions.

Findings

Critical exponents are identical for classical and quantum systems studied.

Analytical solutions of geodesic equations near singularities are obtained.

Evidence suggests the universality of geometric critical exponents.

Abstract

We define geometric critical exponents for systems that undergo continuous second order classical and quantum phase transitions. These relate scalar quantities on the information theoretic parameter manifolds of such systems, near criticality. We calculate these exponents by approximating the metric and thereby solving geodesic equations analytically, near curvature singularities of two dimensional parameter manifolds. The critical exponents are seen to be the same for both classical and quantum systems that we consider, and we provide evidence about the possible universality of our results.