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.

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

References in corpus (5)

• Novel type of phase transition in a system of self-driven particles
• Nonmutual torques and the unimportance of motility for long-range order in two-dimensional flocks
• A novel nonequilibrium state of matter: a $d=4-\epsilon$ expansion study of Malthusian flocks
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Cited by in corpus (9)

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• Signatures of irreversibility in microscopic models of flocking
• Alignment Destabilizes Crystal Orders in Active Systems
• Minimum scaling model and exact exponents for the Nambu-Goldstone modes in the Vicsek Model
• Reentrant phase behavior in binary topological flocks with nonreciprocal alignment
• Mechanical inhibition of dissipation in a thermodynamically consistent active solid
• Emergent centrality in rank-based supplanting process