Thermodynamics of cosmic string densities in U(1) scalar field theory

We present a full characterization of the phase transition in U(1) scalar field theory and of the associated vortex string thermodynamics in 3D. We show that phase transitions in the string densities exist and measure their critical exponents, both far the long string and the short loops. Evidence for a natural separation between these two string populations is presented. In particular, our results strongly indicate that an infinite string population will only exist above the critical temperature. Canonical initial conditions for cosmic string evolution are shown to correspond to the infinite temperature limit of the theory. [S0031-9007(97)05189-2].