Dynamics of random dipoles : chaos {\it vs} ferromagnetism

TL;DR

This paper investigates the microcanonical dynamics of random magnetic dipoles, revealing a transition between chaotic paramagnetic and integrable ferromagnetic phases, with a simple criterion for the transition and analysis of critical behavior.

Contribution

It introduces a numerical criterion for the phase transition and characterizes the critical exponents near the transition point.

Findings

Identified a transition between chaotic and integrable phases.

Formulated a simple criterion for the phase transition.

Numerically determined critical exponents near the transition.

Abstract

The microcanonical dynamics of an ensemble of random magnetic dipoles in a needle has been investigated. Analyzing magnetic reversal times, a transition between a chaotic paramagnetic phase and an integrable ferromagnetic phase has been numerically found. In particular, a simple criterium for transition has been formulated. Close to the transition point the statistics of average magnetic reversal times and fluctuations have been studied and critical exponents numerically given.