XY Model with Persistent Noise

TL;DR

This paper studies a 2D XY model with persistent, time-correlated noise, revealing that it maintains quasi-order despite rapid noise decay, with a BKT transition whose exponents depend on noise persistence.

Contribution

It introduces a persistent noise variant of the XY model, showing altered critical behavior and transition properties compared to equilibrium models.

Findings

Model remains quasi-ordered despite fast-decaying correlations

BKT transition persists with modified scaling exponents

Critical behavior depends on noise persistence time

Abstract

We consider a 2D XY model subjected to time-correlated noise, a model of direct relevance to active crystals, which were shown recently to be able to support very large deformations without melting in the presence of persistent fluctuations. We find that our persistent XY model can remain quasi-ordered in spite of correlations decaying much faster than allowed in equilibrium. We then investigate theoretically and numerically the order-disorder transition and conclude that it remains of the Berezinskii-Kosterlitz-Thouless type, but with scaling exponents that vary with the persistence time of the noise.