Fluctuation-Induced First Order Transition to Collective Motion

The nature of the transition to collective motion in assemblies of aligningself-propelled particles remains a long-standing matter of debate. In thisarticle, we focus on dry active matter and show that weak fluctuations sufficeto generically turn second-order mean-field transitions into a `discontinuous'coexistence scenario. Our theory shows how fluctuations induce adensity-dependence of the polar-field mass, even when this effect is absent atmean-field level. In turn, this dependency on density triggers a feedback loopbetween ordering and advection that ultimately leads to an inhomogeneoustransition to collective motion and the emergence of non-linear travelling`flocks'. Importantly, we show that such a fluctuation-induced first ordertransition is present in both metric models, in which particles align withneighbors within a finite distance, and in topological ones, in which alignmentis not based on relative distances. We compute analytically the noise-inducedrenormalization of the polar-field mass using stochastic calculus, which wefurther back up by a one-loop field-theoretical analysis. Finally, we confirmour analytical predictions by numerical simulations of fluctuatinghydrodynamics as well as of topological microscopic models with eitherk-nearest neighbors or Voronoi alignment.