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

Oriana K. Diessel; Jaewon Kim; Ehud Altman

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arXiv · 2507.01959

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

Oriana K. Diessel·Jaewon Kim·Ehud Altman

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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.

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BibTeX RIS

Oriana K. Diessel, Jaewon Kim, Ehud Altman. 2025-07-02. Stabilization of long-range order in low-dimensional nonequilibrium $O(N)$ models. https://arxiv.org/abs/2507.01959

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