English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We study the order-disorder transition in two-dimensional incompressiblesystems of motile particles with alignment interactions through extensivenumerical simulations of the incompressible Toner-Tu (ITT) field theory and adetailed finite-size scaling (FSS) analysis. The transition looks continuous inthe explored parameter space, but the effective susceptibility exponent$\gamma/\nu$ and the dynamic exponent $z$ exhibit a strong, non-monotonicvariation on the system size in the form of double crossovers. At small sizes,mean-field exponents are observed for the homogeneous $k=0$ mode whereasspatial fluctuations follow Gaussian statistics. A first crossover marks thedeparture from this regime to one where the system behaves like the equilibriumXY model with long-ranged dipolar interaction and vortex excitations. At largersizes, scaling deviates from the dipolar XY behavior and a second crossover isobserved, to presumably the asymptotic ITT universality class. At thiscrossover to genuinely off-equilibrium behavior, advection comes in to expeditetransport of fluctuations, suppress large-scale fluctuations and help stabilizelong-range order. We obtain estimates and bounds of the universal Bindercumulant and exponents of the ITT class. We propose a reduced hydrodynamictheory, previously overlooked, that quantitatively describes the first scalingregime. By providing a relatively comprehensive numerical picture and a novelanalytical description, our results help elucidate finite-size effects incritical active matter systems, which have been argued to be relevant forunderstanding scale-free behavior in real flocks or swarms.

Finite-size scaling and double-crossover critical behavior in two-dimensional incompressible polar active fluids