Flocking in One Dimension: Asters and Reversals

TL;DR

This paper investigates the one-dimensional active Ising model, revealing phases with moving flocks and static asters, analyzing their dynamics, shapes, and reversal behaviors through simulations and theoretical models.

Contribution

It introduces a detailed study of flocking and aster phases in 1D active Ising models, combining simulations with mean-field theory to understand their dynamics and structures.

Findings

Flocking phase features large, ballistic, reversibly moving aggregates.

Aster phase consists of immobile, dense, opposite-magnetization aggregates.

Reversal times and coarsening dynamics follow extremal and mean-field behaviors.

Abstract

We study the one-dimensional active Ising model in which aligning particles undergo diffusion biased by the signs of their spins. The phase diagram obtained varying the density of particles, their hopping rate and the temperature controlling the alignment shows a homogeneous disordered phase but no homogeneous ordered one, as well as two phases with localized dense structures. In the flocking phase, large ordered aggregates move ballistically and stochastically reverse their direction of motion. In what we termed the "aster" phase, dense immobile aggregates of opposite magnetization face each other, exchanging particles, without any net motion of the aggregates. Using a combination of numerical simulations and mean-field theory, we study the evolution of the shapes of the flocks, the statistics of their reversal times, and their coarsening dynamics. Solving exactly for the zero-temperature dynamics of an aster allows us to understand their coarsening, which shows extremal dynamics, while mean-field equations account for their shape.