Active XY model on a substrate: Density fluctuations and phase ordering

Abstract

We explore the generic long wavelength properties of an active XY model on a substrate, consisting of collection of nearly phase-ordered active XY spins in contact with a diffusing, conserved species, as a representative system of active spinners with a conservation law. The spins rotate actively in response to the local density fluctuations and local phase differences, on a solid substrate. We investigate this system by Monte-Carlo simulations of an agent-based model, which we set up, complemented by the hydrodynamic theory for the system. We demonstrate that this system can phase-synchronize without any hydrodynamic interactions. Our combined numerical and analytical studies show that this model, when stable, displays hitherto unstudied scaling behavior: As a consequence of the interplay between the mobility, active rotation and number conservation, such a system can be stable over a wide range of the model parameters characterized by a novel correspondence between the phase and density fluctuations. In different regions of the phase space where the phase-ordered system is stable, it shows phase ordering which is generically either logarithmically stronger than the conventional quasi long range order (QLRO) found in its equilibrium limit, together with "miniscule number fluctuations", or logarithmically weaker than QLRO along with "giant number fluctuations", showing a novel one-to-one correspondence between phase ordering and density fluctuations in the ordered states. Intriguingly, these scaling exponents are found to depend explicitly on the model parameters. We further show that in other parameter regimes there are no stable, ordered phases. Instead, two distinct types of disordered states with short range phase-order are found, characterized by the presence or absence of stable clusters of finite sizes.

arXiv comment58 pages, companion long paper of arXiv:2104.10982, supplemental movies available on request, To be appeared in Phys. Rev. E

References in corpus (49)

• Novel type of phase transition in a system of self-driven particles
• Synchronization in complex networks
• Quantum fluids of light
• Motility-Induced Phase Separation
• Flocks, herds, and schools: A quantitative theory of flocking
• Local Density Fluctuations, Hyperuniformity, and Order Metrics
• Hyperuniform States of Matter
• Turning bacteria suspensions into a "superfluid"
• Spontaneous Oscillations of Collective Molecular Motors
• The Physics of the Vicsek Model
• Synchronization and Collective Dynamics in a Carpet of Microfluidic Rotors
• Spatiotemporal order and emergent edge currents in active spinner materials
• Theories of Binary Fluid Mixtures: From Phase-Separation Kinetics to Active Emulsions
• Cell body rocking is a dominant mechanism for flagellar synchronization in a swimming alga
• Hydrodynamic phase-locking of swimming microorganisms
• Activity induced synchronization: From Mutual Flocking to Chiral Self-Sorting
• Collective synchronization in spatially extended systems of coupled oscillators with random frequencies
• Are Steadily Moving Crystals Unstable?
• Active nematics are intrinsically phase-separated
• Realizing the physics of motile cilia synchronization with driven colloids
• Symmetric shear banding and swarming vortices in bacterial "superfluids"
• Strong Phase Separation in a Model of Sedimenting Lattices
• Hydrodynamic Instabilities Provide A Generic Route To Spontaneous Biomimetic Oscillations In Chemomechanically Active Filaments
• Synchronization in A Carpet of Hydrodynamically Coupled Rotors with Random Intrinsic Frequency
• Hyperuniformity and phase enrichment in vortex and rotor assemblies
• Phase Dependent Forcing and Synchronization in the three-sphere model of Chlamydomonas
• Mobility induces global synchronization of oscillators in periodic extended systems
• Synchronization in dynamical networks of locally coupled self-propelled oscillators
• Hydrodynamic synchronization of spontaneously beating filaments
• Active Matter Class with Second-Order Transition to Quasi-Long-Range Polar Order
• Lattice duality for the compact Kardar-Parisi-Zhang equation
• Chiral active hexatics: Giant number fluctuations, waves and destruction of order
• Collective behavior of Vicsek particles without and with obstacles
• Synchronisation and liquid crystalline order in soft active fluids
• The Phase Synchronized State of Oriented Active Fluids
• Defects Superdiffusion and Unbinding in a 2D XY Model of Self-Driven Rotors
• Novel universality classes of coupled driven diffusive systems
• Mean Magnetic Field and Noise Cross-Correlation in Magnetohydrodynamic Turbulence: Results from a One-Dimensional Model
• Scaling and universality in coupled driven diffusive models
• Marching on a rugged landscape: Universality in disordered asymmetric exclusion processes
• Active hydrodynamics of synchronization and ordering in moving oscillators
• Kinetic roughening in active interfaces
• Broken living layers: dislocations in active smectics
• Mobility-induced order in active XY spins on a substrate
• Statistical mechanics of phase transitions in elastic media with vanishing thermal expansion
• Disorders can induce continuously varying universal scaling in driven systems
• Stiffening or softening of elastic media: Anomalous elasticity near phase transitions
• Dynamic scaling in the quenched disordered classical $N$-vector model
• The Critical Properties of Two-dimensional Oscillator Arrays

Cited by in corpus (4)

• Mobility-induced order in active XY spins on a substrate
• Kardar-Parisi-Zhang scaling in time-crystalline matter
• 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