The Non--Ergodicity Threshold: Time Scale for Magnetic Reversal

TL;DR

This paper establishes a non-ergodicity threshold in a classical Heisenberg model, showing how it affects magnetic reversal times and phase transitions, with implications for finite system dynamics.

Contribution

It introduces the concept of a non-ergodicity threshold in a classical spin model and analyzes its impact on magnetic reversal dynamics and phase transition predictions.

Findings

Magnetization reversal time diverges at the threshold as a power law.

Below the threshold, the energy surface is disconnected with distinct magnetization components.

The non-ergodicity threshold influences finite system dynamics and phase transition behavior.

Abstract

We prove the existence of a non-ergodicity threshold for an anisotropic classical Heisenberg model with all-to-all couplings. Below the threshold, the energy surface is disconnected in two components with positive and negative magnetizations respectively. Above, in a fully chaotic regime, magnetization changes sign in a stochastic way and its behavior can be fully characterized by an average magnetization reversal time. We show that statistical mechanics predicts a phase--transition at an energy higher than the non-ergodicity threshold. We assess the dynamical relevance of the latter for finite systems through numerical simulations and analytical calculations. In particular, the time scale for magnetic reversal diverges as a power law at the ergodicity threshold with a size-dependent exponent, which could be a signature of the phenomenon.