CORRELATIONS IN 2-DIMENSIONAL VORTEX LIQUIDS

We report on a high-temperature perturbation expansion study of the su perfluid-density spatial correlation function of a Ginzburg-Landau-mod el superconducting film in a magnetic field. We have derived a closed form which expresses the contribution to the correlation function from each graph of the perturbation theory in terms of the number of Euler paths around appropriate subgraphs. We have enumerated all graphs app earing out to 12th order in the expansion and have evaluated their con tributions to the correlation function, Low-temperature correlation fu nctions, obtained using Pade approximants, are in good agreement with Monte Carlo simulation results and show that the vortex liquid becomes strongly correlated at temperatures well above the vortex solidificat ion temperature. We have also evaluated the high-temperature expansion for the free energy of the Ginzburg-Landau model to 13th order, two o rders further than in previous work.