Classical Infinite-Range-Interaction Heisenberg Ferromagnetic Model: Metastability and Sensitivity to Initial Conditions

TL;DR

This paper investigates a classical Heisenberg ferromagnet with infinite-range interactions, revealing metastability and initial condition sensitivity through numerical microcanonical ensemble simulations, extending understanding of phase transitions in such systems.

Contribution

It introduces a modified inertial classical Heisenberg model with infinite-range interactions and analyzes its metastability and sensitivity to initial conditions via molecular dynamics simulations.

Findings

Identification of metastable states in the model.

Observation of sensitivity to initial conditions.

Confirmation of second-order phase transition.

Abstract

A N-sized inertial classical Heisenberg ferromagnet, which consists in a modification of the well-known standard model, where the spins are replaced by classical rotators, is studied in the limit of infinite-range interactions. The usual canonical-ensemble mean-field solution of the inertial classical $n$-vector ferromagnet (for which $n=3$ recovers the particular Heisenberg model considered herein) is briefly reviewed, showing the well-known second-order phase transition. This Heisenberg model is studied numerically within the microcanonical ensemble, through molecular dynamics.