Coupling spin to velocity: collective motion of Hamiltonian polar particles

Abstract

We propose a conservative two-dimensional particle model in which particles carry a continuous and classical spin. The model includes standard ferromagnetic interactions between spins of two different particles, and a nonstandard coupling between spin and velocity of the same particle inspired by the coupling observed in self-propelled hard discs. Because of this coupling Galilean invariance is broken and the conserved linear momentum associated to translation invariance is not proportional to the velocity of the center of mass. Also, the dynamics is not invariant under a global rotation of the spins alone. This, in principle, leaves room for collective motion and thus raises the question whether collective motion can arise in Hamiltonian systems. We study the statistical mechanics of such a system, and show that, in the fully connected (or mean-field) case, a transition to collective motion does exist in spite of momentum conservation. Interestingly, the velocity of the center of mass, which in the absence of Galilean invariance, is a relevant variable, also feeds back on the magnetization properties, as it acts as an external magnetic field that smoothens the transition. Molecular dynamics simulations of finite size systems indeed reveal a rich phase diagram, with a transition from a disordered to a homogeneous polar phase, but also more complex inhomogeneous phases with local order interrupted by topological defects.

References in corpus (7)

• Novel type of phase transition in a system of self-driven particles
• Interaction Ruling Animal Collective Behaviour Depends on Topological rather than Metric Distance: Evidence from a Field Study
• Emergence of macroscopic directed motion in populations of motile colloids
• Collective motion of self-propelled particles interacting without cohesion
• Self-propulsion of pure water droplets by spontaneous Marangoni stress driven motion
• Flocking at a distance in active granular matter
• Flocking and turning: a new model for self-organized collective motion

Cited by in corpus (8)

• Dynamics of a self-propelled particle in a harmonic trap
• Effective temperatures in inhomogeneous passive and active bidimensional Brownian particle systems
• Velocity and Speed Correlations in Hamiltonian Flocks
• Hohenberg-Mermin-Wagner type theorems for equilibrium models of flocking
• Ferromagnetism-induced Phase Separation in a Two-dimensional Spin Fluid
• Coupling an elastic string to an active bath: the emergence of inverse damping
• The BKT Transition and its Dynamics in a Spin Fluid
• The Inertial Spin Model of flocking with position-dependent forces