Effective equilibrium picture in $xy-$model with exponentially correlated noise

TL;DR

This paper investigates how exponentially correlated noise influences the $xy$-model, revealing that memory effects enhance ordering in mean-field but do not alter the topological transition temperature in two dimensions, supported by theoretical and numerical analysis.

Contribution

It introduces an effective equilibrium framework for the $xy$-model under correlated noise, showing how noise correlation time affects phase transitions.

Findings

Critical temperature increases with noise correlation in mean-field

Topological transition temperature remains unchanged in 2D

Finite size effects cause a crossover in vortex proliferation

Abstract

We study the effect of exponentially correlated noise on $xy-$model in the limit of small correlation time discussing the order-disorder transition in mean-field and the topological transition in two dimensions. We map the steady states of the non-equilibrium dynamics into an effective equilibrium theory. In mean-field, the critical temperature increases with the noise correlation time $\tau$ indicating that memory effects promote ordering. This finding is confirmed by numerical simulations. The topological transition temperature in two dimensions remains untouched. However, finite size effects induce a crossover in the vortices proliferation that is confirmed by numerical simulations.