Chaotic properties of spin lattices near second-order phase transitions

TL;DR

This paper numerically studies the chaotic behavior of classical spin lattices near phase transitions, revealing a characteristic peak in the Lyapunov spectrum shape called the G-index, and introduces a new algorithm for temperature determination in such systems.

Contribution

It introduces the G-index as a new characteristic of Lyapunov spectra near phase transitions and proposes a general temperature determination algorithm for many-particle systems.

Findings

G-index peaks sharply at phase transition temperature

Lyapunov spectra shape correlates with phase transition

New algorithm for temperature measurement in systems without kinetic energy

Abstract

We perform a numerical investigation of the Lyapunov spectra of chaotic dynamics in lattices of classical spins in the vicinity of second-order ferromagnetic and antiferromagnetic phase transitions. On the basis of this investigation, we identify a characteristic of the shape of the Lyapunov spectra, the "G-index", which exhibits a sharp peak as a function of temperature at the phase transition, provided the order parameter is capable of sufficiently strong dynamic fluctuations. As a part of this work, we also propose a general numerical algorithm for determining the temperature in many-particle systems, where kinetic energy is not defined.