Stabilization of long-range order in low-dimensional nonequilibrium $O(N)$ models

TL;DR

This paper introduces a novel mechanism involving non-Markovian dissipation and slow modes that enables the stabilization of long-range order in low-dimensional nonequilibrium $O(N)$ models, circumventing the Mermin-Wagner theorem.

Contribution

It identifies a new mechanism combining non-Markovian dissipation and conservation laws to stabilize long-range order in low-dimensional nonequilibrium systems.

Findings

Non-Markovian dissipation alone is insufficient for long-range order.

Interplay with slow modes due to conservation laws stabilizes order.

Mechanism extends understanding of symmetry breaking in nonequilibrium models.

Abstract

It is now well established that the Mermin-Wagner theorem can be circumvented in nonequilibrium systems, allowing for the spontaneous breaking of a continuous symmetry and the emergence of long-range order in low dimensions. However, only a few models demonstrating this violation are known, and they often rely on specific mechanisms that may not be generally applicable. In this work, we identify a new mechanism for nonequilibrium-induced long-range order in a class of $O(N)$-symmetric models. Inspired by the role of long-range spatial interactions in equilibrium, consider the effect of non-Markovian dissipation, in stabilizing long range order in low-dimensional nonequilibrium systems. We find that this alone is insufficient, but the interplay of non-Markovian dissipation and slow modes due to conservation laws can effectively suppress fluctuations and stabilize long-range order.