First-order fluctuation-induced phase transitions to collective motion
The transition to collective motion is paradigmatic of active matter. Self-propelled particles that stochastically align undergo a transition between a disordered state, at low density and large noise, and an ordered one, at high density and low noise. In the latter phase, particles travel together in a randomly selected direction of space, hence spontaneously breaking its isotropy. The nature of this transition has been at the center of a long-standing debate. Numerical simulations and mean-fieldish continuous descriptions have led to the common belief that, depending on the type of microscopic interactions between particles, two types of transitions could be observed. When particles interact with their neighbours within a finite-distance, the transition is first order, with a coexistence phase separating the disordered gas and the ordered liquid. On the contrary, when particles interact with `toplogical' neighbours, the transition is believed to be continuous. In this talk I will show how dressing mean-field hydrodynamic descriptions with noise systematically lead to first-order phase transitions. This holds for metric models but, more surprisingly, also for topological hydrodynamic theories that retain the non-local nature of the aligning interactions at the macroscopic scale. These results have been confirmed using numerical simulations of microscopic models in which particles interact with their k nearest neighbours, a model which is claimed to be relevant for animal-behaviour studies.
This is a weekly series of informal talks focussing on some theoretical aspect of Condensed Matter, Biological, and Statistical Physics..