ICMCS Seminar - Mermin-Wagner Strikes Back: The Breakdown of Flocks

Collective motion is found everywhere in nature, whether that be flocks of birds, schools of fish, or suspensions of swimming bacteria. In recent decades, it has also been extensively studied by scientists as an example of an “active matter” phenomenon that breaks much of the intuition we might carry over from traditional soft matter physics. The most famous minimal model for this was proposed by Vicsek et al. in 1995, with point particles that move at constant speed and align with their neighbours, while experiencing fluctuations in their orientation.

This simple model produced a ground-breaking result – the existence of a “flocked” state with long-range orientational order, breaking a continuous rotational symmetry in two dimensions. Such behaviour is forbidden in equilibrium by the Mermin-Wagner theorem, and it helped to launch the study of active matter within statistical physics.

In our work, we consider a related model that is expected to fall under the same universality class. By leveraging very large-scale simulations of both individual particles and coarse-grained fields, we identify previously unreported phases and find that the flocked state breaks down in the asymptotic limit.

Our results indicate that the main assumptions underpinning the field of active matter may need to be revaluated.

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