  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 for 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 show to correspond to the infinite temperature limit of the
theory.
