Critical Exponent for the Lyapunov Exponent and Phase Transitions -- The Generalized Hamiltonian Mean-Field Model

TL;DR

This paper investigates the behavior of the largest Lyapunov exponent near phase transitions in a long-range interacting system, revealing a potential universal critical exponent for second-order transitions and differences for first-order ones.

Contribution

It extends previous models to a generalized Hamiltonian mean-field system, providing semi-analytic and numerical estimates of the Lyapunov exponent and identifying critical exponents near phase transitions.

Findings

Critical exponent for second-order phase transitions suggests universality.

Different critical exponent observed for first-order phase transitions.

Lyapunov exponent decays as a power law near second-order transitions.

Abstract

We compute semi-analytic and numerical estimates for the largest Lyapunov exponent in a many-particle system with long-range interactions, extending previous results for the Hamiltonian Mean Field model with a cosine potential. Our results evidence a critical exponent associated to a power law decay of the largest Lyapunov exponent close to second-order phase-transitions, close to the same value as for the cosine Hamiltonian Mean Field model, suggesting the possible universality of this exponent. We also show that the exponent for first-order phase transitions has a different value from both theoretical and numerical estimates.