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 nonperturbative thermodynamics of scalar U(1) field theory in 3D. All parameters characterizing the length distributions exhibit critical behavior at Tc 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.