Non-equilibrium quasi-long-range order of driven random field O(N) model

TL;DR

This paper studies driven three-dimensional O(N) models with random fields, revealing a non-equilibrium quasi-long-range order phase with power-law correlations and a transition similar to the Kosterlitz-Thouless transition.

Contribution

It demonstrates the existence of a non-equilibrium quasi-long-range order and a Kosterlitz-Thouless-like transition in driven 3D O(N) models with random fields, using analytical and numerical methods.

Findings

Power-law decay of correlations in driven N=2 model.

Identification of a non-equilibrium phase transition.

Resemblance to Kosterlitz-Thouless transition in 2D XY model.

Abstract

We investigate three-dimensional O(N) spin models driven with a uniform velocity over a random field. Within a spin-wave approximation, it is shown that in the strong driving regime the model with N=2 exhibits a quasi-long-range order in which the spatial correlation function decays in a power-law form. Furthermore, for the cases that N=2 and 3, we numerically demonstrate a non-equilibrium phase transition between the quasi-long-range order phase and the disordered phase, which turns out to resemble the Kosterlitz-Thouless transition in the two-dimensional pure XY model in equilibrium.