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Condensed Matter > Statistical Mechanics
Title: Correlated Noise and Critical Dimensions
(Submitted on 27 Feb 2023 (v1), revised 21 Mar 2023 (this version, v2), latest version 9 Oct 2023 (v6))
Abstract: In equilibrium, the Mermin-Wagner theorem prohibits the continuous symmetric breaking for all dimensions $d\leq 2$. In this work, we discuss that this limitation can be circumvented in non-equilibrium systems driven by spatially or temporally long-range anticorrelated noise. We first compute the lower and upper critical dimensions of the $\phi^4$ model driven by spatio-temporally correlated noise by means of the dimensional analysis. Next, we consider the spherical model, which corresponds to the large $n$ limit of the $O(n)$ model and allows us to compute the critical dimensions analytically. Both results suggest that the critical dimensions increase when the noise is positively correlated in space and time, and decrease when anticorrelated. We also report that the spherical model with the correlated noise shows the hyperuniformity and giant number fluctuation even well above the critical point.
Submission history
From: Harukuni Ikeda [view email][v1] Mon, 27 Feb 2023 11:05:09 GMT (26kb)
[v2] Tue, 21 Mar 2023 06:13:04 GMT (29kb)
[v3] Wed, 22 Mar 2023 02:41:18 GMT (29kb)
[v4] Wed, 5 Apr 2023 05:52:32 GMT (29kb)
[v5] Thu, 3 Aug 2023 09:54:30 GMT (275kb,D)
[v6] Mon, 9 Oct 2023 11:14:33 GMT (276kb,D)
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