Existence of long-range order in the steady state of a two dimensional, two-temperature XY model

TL;DR

This paper demonstrates through simulations that a two-dimensional two-temperature XY model exhibits a continuous phase transition to a long-range ordered state in nonequilibrium conditions, challenging traditional equilibrium theorems.

Contribution

It provides evidence of long-range order in a nonequilibrium 2D XY model, showing the failure of the Mermin-Wagner theorem extension in such systems.

Findings

Long-range order appears in the steady state.

The phase transition is continuous.

Effective dipole interactions drive ordering.

Abstract

Monte Carlo simulations are used to show that the steady state of the d=2, two-temperature, diffusive XY model displays a continuous phase transition from a homogeneous disordered phase to a phase with long-range order. The long-range order exists although both the dynamics and the interactions are local, thus indicating the failure of a naive extension of the Mermin-Wagner theorem to nonequilibrium steady states. It is argued that the ordering is due to effective dipole interactions generated by the nonequilibrium dynamics.