Mobility-induced order in active XY spins on a substrate

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.

arXiv comment7 pages,companion short paper of ArXiv: 2105.03919 (2021), Supplementary movies available on request, To appear in Phys. Rev. E Letter

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• Logarithmic or algebraic: roughening of an active Kardar-Parisi-Zhang surface
• Defect-Mediated Aggregation and Motility-Induced Phase Separation in Self-Propelled Lattice-Gas Active XY Model