Thermodynamics of Gauge-Invariant U(1) Vortices from Lattice Monte Carlo   Simulations
  We study non-perturbatively and from first principles the thermodynamics of vortices in 3d U(1) gauge+Higgs theory, or the Ginzburg-Landau model, which has frequently been used as a model for cosmological topological defect formation. We discretize the system and introduce a gauge-invariant definition of a vortex passing through a loop on the lattice. We then study with Monte Carlo simulations the total vortex density, extract the physically meaningful part thereof, and demonstrate that it has a well-defined continuum limit. The total vortex density behaves as a pseudo order parameter, having a discontinuity in the regime of first order transitions and behaving continuously in the regime of second order transitions. Finally, we discuss further gauge-invariant observables to be measured. 
K. Kajantie, M. Karjalainen, M. Laine, J. Peisa and A. Rajantie