STATISTICAL-MECHANICS OF VORTICES

The equation of state for vortices in the abelian Higgs model is deriv ed, assuming that the vortices are at critical coupling and that they move on a large sphere. The vortex dynamics is assumed to be well appr oximated by geodesic motion through the parameter space of static mult i-vortex solutions of the Bogomolny equations. The partition function essentially depends only on the volume of this parameter space. The eq uation of state for the vortices is of the Clausius form P(A - 4piN) = NT, where P is the pressure, A the area of the sphere, N the number o f vortices and T the temperature.