The length distribution of vortex strings in U(1) equilibrium scalar   field theory
  We characterize the statistical length distribution of vortex strings by studying the non-perturbative thermodynamics of scalar U(1) field theory in 3D. All parameters characterizing the length distributions exhibit critical behavior at $T_c$ and we measure their associated critical exponents. Moreover we show that vortex strings are generally self-seeking at finite temperature and that there exists a natural separation between long strings and small loops based on their spatial correlation behavior. 
N.D. Antunes (U. of Sussex) and L.M.A. Bettencourt (Los Alamos)