A system of thermally fluctuating flux lines with short-range interaction is considered. The flux lines are described by fermions coupled to a gauge field. Three different phases are found in mean-field theory for the gauge field: at low temperatures there is an Abrikosov flux-line lattice and a Meissner phase, and the high-temperature phase is an entangled liquid of flux lines.
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Feigel’man et al. (1992) studied this question.
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