Rotating states in driven clock- and XY-models

TL;DR

This paper investigates the behavior of 3D driven active rotator models with XY-type interactions, revealing phase transitions and unique stationary states under non-equilibrium conditions.

Contribution

It provides a theoretical analysis of driven clock- and XY-models, including conjectures on phase regimes and proof of unique stationary distribution in non-ergodic dynamics.

Findings

Low-temperature perturbation of equilibrium behavior

Emergence of massless modes and synchronized rotation

Existence of a unique stationary distribution despite non-ergodicity

Abstract

We consider 3D active plane rotators, where the interaction between the spins is of XY-type and where each spin is driven to rotate. For the clock-model, when the spins take N\gg1 possible values, we conjecture that there are two low-temperature regimes. At very low temperatures and for small enough drift the phase diagram is a small perturbation of the equilibrium case. At larger temperatures the massless modes appear and the spins start to rotate synchronously for arbitrary small drift. For the driven XY-model we prove that there is essentially a unique translation-invariant and stationary distribution despite the fact that the dynamics is not ergodic.