Mobility-induced order in active XY spins on a substrate

TL;DR

This paper demonstrates that active XY spins coupled with a diffusing species on a substrate can exhibit stable, non-equilibrium ordered phases with unique quasi-long-range order and fluctuation properties, depending on system parameters.

Contribution

It introduces a minimal theoretical model for active spinners showing stable ordered phases with tunable fluctuation characteristics, extending understanding of active matter systems.

Findings

Stable uniform phases with generalized QLRO and hyperuniform or giant fluctuations.

Nonuniversal scaling of phase and density fluctuations based on nonlinear couplings.

Absence of stable order in certain parameter regimes.

Abstract

We elucidate that the nearly phase-ordered active XY spins in contact with a conserved, diffusing species on a substrate can be stable. For wide-ranging model parameters, it has stable uniform phases robust against noises. These are distinguished by generalized quasi-long range (QLRO) orientational order logarithmically stronger or weaker than the well-known QLRO in equilibrium, together with miniscule (i.e., hyperuniform) or giant number fluctuations, respectively. This illustrates a direct correspondence between the two. The scaling of both phase and density fluctuations in the stable phase-ordered states is nonuniversal: they depend on the nonlinear dynamical couplings. For other parameters, it has no stable uniformly ordered phase. Our model, a theory for active spinners, provides a minimal framework for wide-ranging systems, e.g., active superfluids on substrates, synchronization of oscillators, active carpets of cilia and bacterial flagella and active membranes.