Correlations between two vortices in dry active matter

It was recently shown that wet active matter can form synchronized rotating vortices in a square lattice, similar to an antiferromagnetic Ising model (by considering rotation direction as spin projection). In this study, we investigate whether such a correlated state occurs for a model of dry active matter. We achieve that by numerically simulating the dynamics of a system of active particles in the presence of two identical circular obstacles. Then, we measure the angular velocity correlation function of both vortices as a function of the obstacle diameter, their shortest separation (gap), and the particle density. When the correlation function is negative, both vortices rotate in contrary directions. They maintain this state by exchanging particles through the region between them, analogously to synchronized cogs. On the other hand, with a positive correlation function, a single rotating cluster emerges, and the particles move around the whole structure, similar to a belt strapped around the obstacles. Additionally, we observe the emergence of uncorrelated states at the transition between correlated states, in which only a single vortex is present, or in the large gap regime, in which the vortices are nearly independent on each other.