Susceptibility of Polar Flocks to Spatial Anisotropy

TL;DR

This paper investigates how spatial anisotropy affects polar flocks in two-dimensional active models, revealing that even minimal anisotropy drastically alters collective behavior, destroying long-range order and changing the nature of traveling bands.

Contribution

It demonstrates that spatial anisotropy fundamentally changes the phenomenology of polar flocks in active models, contrasting with passive cases, and provides a scaling argument explaining this difference.

Findings

Anisotropy destroys long-range correlations in large systems.

Traveling bands become a single moving domain under anisotropy.

A finite system with large q exhibits Vicsek-like phenomenology.

Abstract

We consider the effect of spatial anisotropy on polar flocks by investigating active $q$-state clock models in two dimensions. In contrast to what happens in equilibrium, we find that, in the large-size limit, any amount of anisotropy changes drastically the phenomenology of the rotationally-invariant case, destroying long-range correlations, pinning the direction of global order, and transforming the traveling bands of the coexistence phase into a single moving domain. All this happens beyond a lengthscale that diverges in the $q\to\infty$ limit. A phenomenology akin to that of the Vicsek model can thus be observed in a finite system for large enough values of $q$. We provide a scaling argument which rationalizes why anisotropy has so different effects in the passive and active cases.