Hohenberg-Mermin-Wagner type theorems for equilibrium models of flocking
Abstract
We study a class of two-dimensional models of classical hard-core particles with Vicsek-type "exchange interaction" that aligns the directions of motion of nearby particles. By extending the Hohenberg-Mermin-Wagner theorem for the absence of spontaneous magnetization and the McBryan-Spencer bound for correlation functions, we prove that the models do not spontaneously break the rotational symmetry in their equilibrium states at any nonzero temperature. We thus conclude that the mobility of particles alone does not account for the spontaneous symmetry breaking in Vicsek type models. The origin of the symmetry breaking must be sought in the absence of detailed balance condition, or, equivalently, in the nonequilibrium nature.
Keywords
Cite
@article{arxiv.2008.02698,
title = {Hohenberg-Mermin-Wagner type theorems for equilibrium models of flocking},
author = {Hal Tasaki},
journal= {arXiv preprint arXiv:2008.02698},
year = {2020}
}
Comments
8 pages. Refs. [27,28,29] were added and the discussion was improved in version 2. Supplemental material, which should be useful, and Ref [18] are added in version 3. There is a 18.5 minutes video on YouTube in which I discuss the background, motivation, and main results of the present paper: https://youtu.be/CD0WEkNl9XA