Alternating steady state in one-dimensional flocking

TL;DR

This paper investigates a one-dimensional flocking model, revealing a phase transition between condensed and homogeneous states, with a unique alternating steady state where the flock's direction reverses stochastically, preventing spontaneous symmetry breaking.

Contribution

It introduces a lattice model for 1D flocking, characterizes the phase transition, and uncovers the novel alternating steady state with logarithmic reversal times.

Findings

Identifies a continuous phase transition between condensed and homogeneous phases.

Discovers that the condensed phase exhibits stochastic direction reversals.

Reversal times scale logarithmically with system size.

Abstract

We study flocking in one dimension, introducing a lattice model in which particles can move either left or right. We find that the model exhibits a continuous nonequilibrium phase transition from a condensed phase, in which a single `flock' contains a finite fraction of the particles, to a homogeneous phase; we study the transition using numerical finite-size scaling. Surprisingly, in the condensed phase the steady state is alternating, with the mean direction of motion of particles reversing stochastically on a timescale proportional to the logarithm of the system size. We present a simple argument to explain this logarithmic dependence. We argue that the reversals are essential to the survival of the condensate. Thus, the discrete directional symmetry is not spontaneously broken.