Phase Diagram for a 2-D Two-Temperature Diffusive XY Model

TL;DR

This study uses Monte Carlo simulations to map the phase diagram of a two-temperature diffusive XY model, revealing a rich structure of phases and critical lines, including a bicritical point at the equilibrium KT transition.

Contribution

It provides the first detailed phase diagram of a nonequilibrium two-temperature XY model, identifying three phases and characterizing the critical behavior near the KT point.

Findings

Identified three phases: disordered and two ordered with long-range order.

Mapped the nonequilibrium critical lines and their crossover behavior.

Suggested the transition between ordered phases is first-order.

Abstract

Using Monte Carlo simulations, we determine the phase diagram of a diffusive two-temperature XY model. When the two temperatures are equal the system becomes the equilibrium XY model with the continuous Kosterlitz-Thouless (KT) vortex-antivortex unbinding phase transition. When the two temperatures are unequal the system is driven by an energy flow through the system from the higher temperature heat-bath to the lower temperature one and reaches a far-from-equilibrium steady state. We show that the nonequilibrium phase diagram contains three phases: A homogenous disordered phase and two phases with long range, spin-wave order. Two critical lines, representing continuous phase transitions from a homogenous disordered phase to two phases of long range order, meet at the equilibrium the KT point. The shape of the nonequilibrium critical lines as they approach the KT point is described by a crossover exponent of phi = 2.52 \pm 0.05. Finally, we suggest that the transition between the two phases with long-range order is first-order, making the KT-point where all three phases meet a bicritical point.