Equilibrium properties of the condensed states of a turbulent two-dimensional neutral vortex system

Monte Carlo extrapolation methods and approximate evaluations of the partition function are used to obtain the phase transition properties and spatial probability distribution exponents for the Hamiltonian system. A second condensation from dipole pairs to a liquid-like phase is found on cooling the system to a temperature approximately one-tenth the pair condensation temperature. In the condensed dipole pair temperature range the Metropolis algorithm yields dipole configurations similar to those observed in previous numerical integrations of the motion. In the region of the pair condensation transition the distribution of distances between plus and minus vortices follow Levy probability laws over spatial scales extending from the vortex core diameter to the radius of the container enclosing the flow. The joint space-time probability density function for the travel times and lengths of the dipole translation paths between collisions is derived for thermodynamic equilibrium and yields Levy flight like enhanced diffusion. Theoretical values for the diffusion exponent and its temperature dependence are obtained and found to be in agreement with diffusion rates measured during numerical integrations of the vortex motion