Minimum scaling model and exact exponents for the Nambu-Goldstone modes in the Vicsek Model
Soft Condensed Matter
2024-12-19 v2 Statistical Mechanics
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.
Keywords
Cite
@article{arxiv.2403.02086,
title = {Minimum scaling model and exact exponents for the Nambu-Goldstone modes in the Vicsek Model},
author = {Harukuni Ikeda},
journal= {arXiv preprint arXiv:2403.02086},
year = {2024}
}
Comments
5 pages, 1 figure. This paper is a revised version of arXiv:2401.01603 with modified derivation of the scaling exponents