# Coupling spin to velocity: collective motion of Hamiltonian polar particles

@article{Bore2015CouplingST, title={Coupling spin to velocity: collective motion of Hamiltonian polar particles}, author={Sigbj{\o}rn L{\o}land Bore and Michael Schindler and Khanh-Dang Nguyen Thu Lam and Eric Bertin and Olivier Dauchot}, journal={arXiv: Statistical Mechanics}, year={2015} }

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…

## 5 Citations

Velocity and Speed Correlations in Hamiltonian Flocks.

- PhysicsPhysical review letters
- 2020

A 2D Hamiltonian fluid made of particles carrying spins coupled to their velocities exhibits phase coexistence between a collectively moving droplet and a still gas, and the particle displacements within the droplet have remarkably similar correlations to those of birds flocks.

Dynamics of a Self-Propelled Particle in a Harmonic Trap.

- PhysicsPhysical review letters
- 2019

It is shown that self-alignment, taking the form of a torque coupling the particle orientation and velocity, is responsible for the emergence of this second dynamical state for which the particle condensates at a finite distance from the trap center.

Ferromagnetism-induced phase separation in a two-dimensional spin fluid.

- PhysicsThe Journal of chemical physics
- 2019

A detailed finite-size scaling analysis shows that in two dimensions the ferromagnetic phase escapes the Berezinskii-Kosterlitz-Thouless scenario and that the long-range order is not destroyed by the unbinding of topological defects.

Hohenberg-Mermin-Wagner-Type Theorems for Equilibrium Models of Flocking.

- PhysicsPhysical review letters
- 2020

It is proved that two-dimensional Vicsek type models do not spontaneously break the rotational symmetry in their equilibrium states at any nonzero temperature, and suggests that the origin of the symmetry breaking should be sought in the absence of a detailed balance condition, or, equivalently, in nonequilibrium nature.

Effective temperatures in inhomogeneous passive and active bidimensional Brownian particle systems.

- PhysicsPhysical review. E
- 2020

The study of the globally averaged properties is complemented with the theoretical and numerical characterization of the fluctuation distributions of the single-particle diffusion, linear response, and effective temperature in the homogeneous and inhomogeneous phases.

## References

SHOWING 1-10 OF 34 REFERENCES

Flocking and Turning: a New Model for Self-organized Collective Motion

- PhysicsArXiv
- 2014

This work proposes novel dynamical equations for the collective motion of polarized animal groups that account for correlated turning including solely social forces and derives a new model of collective motion based on a generalized coordinates of motion akin to a Hamiltonian formulation for rotations.

Vibrated polar disks: spontaneous motion, binary collisions, and collective dynamics

- Physics
- 2012

We study the spontaneous motion, binary collisions, and collective dynamics of “polar disks”, i.e. specially designed particles which, when vibrated between two horizontal plates, move coherently…

Collective motion of self-propelled particles interacting without cohesion.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2008

The onset of collective motion in Vicsek-style self-propelled particle models in two and three space dimensions is studied in detail and shown to be discontinuous (first-order-like), and the properties of the ordered, collectively moving phase are investigated.

Revisiting the flocking transition using active spins.

- PhysicsPhysical review letters
- 2013

An active Ising model in which spins both diffuse and align on lattice in one and two dimensions is considered, showing that this theoretical prediction holds in 2D whereas the fluctuations alter the transition in 1D, preventing, for instance, any spontaneous symmetry breaking.

Polar patterns of driven filaments

- PhysicsNature
- 2010

A minimal polar-pattern-forming system that consists of highly concentrated actin filaments propelled by immobilized molecular motors in a planar geometry is demonstrated, identifying weak and local alignment interactions to be essential for the observed formation of patterns and their dynamics.

Topological defects and density fluctuations in collectively moving systems

- PhysicsProceedings of the National Academy of Sciences
- 2013

Ensembles of collectively moving particles like flocks of birds, bacteria, or filamentous polymers show a broad range of intriguing phenomena, yet seem to obey very similar physical principles. These…

Emergence of macroscopic directed motion in populations of motile colloids

- PhysicsNature
- 2013

It is reported that dilute populations of millions of colloidal rolling particles self-organize to achieve coherent motion in a unique direction, with very few density and velocity fluctuations, in the polar-liquid state.

Hydrodynamics of soft active matter

- Biology
- 2013

This review summarizes theoretical progress in the field of active matter, placing it in the context of recent experiments, and highlights the experimental relevance of various semimicroscopic derivations of the continuum theory for describing bacterial swarms and suspensions, the cytoskeleton of living cells, and vibrated granular material.

Onset of collective and cohesive motion.

- PhysicsPhysical review letters
- 2004

It is found that this phase transition, in two space dimensions, is always discontinuous, including for the minimal model of Vicsek et al. for which a nontrivial critical point was previously advocated.

Large-scale vortex lattice emerging from collectively moving microtubules

- BiologyNature
- 2012

This study reports experiments in which microtubules are propelled by surface-bound dyneins, providing evidence for the existence of previously unsuspected universality classes of collective motion phenomena.