A Curie-Weiss model with dissipation

TL;DR

This paper studies a mean field spin system with noisy, dissipative interactions, revealing that at low temperatures, the magnetization exhibits spontaneous time-periodic behavior without external forcing.

Contribution

It introduces a stochastic mean field model with dissipative dynamics and demonstrates spontaneous periodic magnetization in the thermodynamic limit at low temperatures.

Findings

Magnetization shows spontaneous time-periodic behavior.

Periodic behavior occurs without external periodic forcing.

Behavior emerges at sufficiently low temperatures.

Abstract

We consider stochastic dynamics for a spin system with mean field interaction, in which the interaction potential is subject to noisy and dissipative stochastic evolution. We show that, in the thermodynamic limit and at sufficiently low temperature, the magnetization of the system has a time periodic behavior, despite of the fact that no periodic force is applied.