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Condensed Matter > Soft Condensed Matter

arXiv:2403.02086 (cond-mat)
[Submitted on 4 Mar 2024 (v1), last revised 20 Nov 2024 (this version, v2)]

Title:Minimum scaling model and exact exponents for the Nambu-Goldstone modes in the Vicsek Model

Authors:Harukuni Ikeda
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Abstract:We investigate the scaling behavior of Nambu-Goldstone (NG) modes in the ordered phase of the Vicsek model, introducing a phenomenological equation of motion (EOM) incorporating a previously overlooked non-linear term. This term arises from the interaction between velocity fields and density fluctuations, leading to new scaling behaviors. We derive exact scaling exponents in two dimensions, which reproduce the isotropic scaling behavior reported in a prior numerical simulation.
Comments: 5 pages, 1 figure. This paper is a revised version of arXiv:2401.01603 with modified derivation of the scaling exponents
Subjects: Soft Condensed Matter (cond-mat.soft); Statistical Mechanics (cond-mat.stat-mech)
Cite as: arXiv:2403.02086 [cond-mat.soft]
  (or arXiv:2403.02086v2 [cond-mat.soft] for this version)
  https://doi.org/10.48550/arXiv.2403.02086

Submission history

From: Harukuni Ikeda [view email]
[v1] Mon, 4 Mar 2024 14:43:29 UTC (70 KB)
[v2] Wed, 20 Nov 2024 02:55:57 UTC (73 KB)
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