# Relaxation to equilibrium in models of classical spins with long-range interactions

## TL;DR

This paper investigates how fluctuations influence the relaxation process of classical Heisenberg spins with long-range interactions, revealing that environmental noise can eliminate quasistationary states and lead to rapid equilibrium attainment.

## Contribution

It demonstrates that environmental fluctuations cause the disappearance of quasistationary states in long-range spin systems, contrasting deterministic and stochastic dynamics.

## Key findings

- Deterministic dynamics exhibit quasistationary states with diverging lifetimes.
- Strong environmental noise induces rapid, size-independent relaxation to equilibrium.
- Glauber Monte Carlo dynamics also show fast relaxation, confirming the effect of fluctuations.

## Abstract

For a model long-range interacting system of classical Heisenberg spins, we study how fluctuations, such as those arising from having a finite system size or through interaction with the environment, affect the dynamical process of relaxation to Boltzmann-Gibbs equilibrium. Under deterministic spin precessional dynamics, we unveil the full range of quasistationary behavior observed during relaxation to equilibrium, whereby the system is trapped in nonequilibrium states for times that diverge with the system size. The corresponding stochastic dynamics, modeling interaction with the environment and constructed in the spirit of the stochastic Landau-Lifshitz-Gilbert equation, however shows a fast relaxation to equilibrium on a size-independent timescale and no signature of quasistationarity, provided the noise is strong enough. Similar fast relaxation is also seen in Glauber Monte Carlo dynamics of the model, thus establishing the ubiquity of what has been reported earlier in particle dynamics (hence distinct from the spin dynamics considered here) of long-range interacting systems, that quasistationarity observed in deterministic dynamics is washed away by fluctuations induced through contact with the environment.