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.

arXiv comment8 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 (19)

• Novel type of phase transition in a system of self-driven particles
• Collective motion
• The Mechanics and Statistics of Active Matter
• Flocks, herds, and schools: A quantitative theory of flocking
• Collective Motion of Vibrated Polar Disks
• Flocking at a distance in active granular matter
• The Physics of the Vicsek Model
• A Reanalysis of the Hydrodynamic Theory of Fluid, Polar-Ordered Flocks
• Long-range nematic order and anomalous fluctuations in suspensions of swimming filamentous bacteria
• Long-range Ordering of Vibrated Polar Disks
• Exact Hydrodynamic Description of Active Lattice Gases
• Nonmutual torques and the unimportance of motility for long-range order in two-dimensional flocks
• Asymmetric exchange in flocks
• Origins and diagnostics of the nonequilibrium character of active systems
• Gliding filament system giving both orientational order and clusters in collective motion
• A novel nonequilibrium state of matter: a $d=4-\epsilon$ expansion study of Malthusian flocks
• Velocity and Speed Correlations in Hamiltonian Flocks
• Coupling spin to velocity: collective motion of Hamiltonian polar particles
• Order by disorder: saving collective motion from topological defects in a conservative model

Cited by in corpus (9)

• Non-reciprocal phase transitions
• Small Obstacle in a Large Polar Flock
• Long-range phase order in two dimensions under shear flow
• 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