Swarmalators with thermal noise

We study of a population of swarmalators, mobile versions of phase oscillators that both sync in time and swarm through space. In particular, we study a XY-type model where the swarmalators run on a 1D ring and are subject to thermal noise. We find four collective states, some of which capture the behavior of real-world swarmalators such as vinegar eels and sperm. Of the four states, the most surprising is the 'mixed state', which blends two of the other states (such mixed states do not occur in Kuramoto model of phase oscillators, for instance). We present the full phase diagram and compute many of the stability boundaries analytically. Being tractable, our model is a natural toy model for studying systems which self-assemble and self-synchronize interdependently.