Correlations in two-dimensional vortex liquids

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Abstract
We report on a high-temperature perturbation expansion study of the superfluid-density spatial correlation function of a Ginzburg-Landau-model 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 appearing out to 12th order in the expansion and have evaluated their contributions to the correlation function. Low-temperature correlation functions, obtained using Padé 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 solidification temperature. We have also evaluated the high-temperature expansion for the free energy of the Ginzburg-Landau model to 13th order, two orders further than in previous work.
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