Melting transition of vortex lattice in point vortex systems

Point vortices take a triangular lattice structure in a rotating system as a minimum energy state. We perform a numerical simulation of point vortex systems using initial conditions indicating that the triangular lattice is randomly perturbed. The total energy increases with the magnitude of the perturbation. When the energy is increased, the vortex lattice becomes irregular and a layered structure appears. When the energy is further increased, the layered structure disappears and a liquidlike state appears. We interpret the melting transition with a mean-field approximation for layered structures.