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Gauge effects on phase transitions in superconductors

Classic and recent results for gauge effects on the properties of the normal-to-superconducting phase transition in bulk and thin film superconductors are reviewed. Similar problems in the description of other natural systems (liquid crystals, quantum field theory, early universe) are also discussed. The relatively strong gauge effects on the fluctuations of the ordering field at low spatial dimensionality D and, in particular, in thin (quasi-2D) films are considered in details. A special attention is paid to the fluctuations of the gauge field. It is shown that the mechanism in which these gauge fluctuations affect on the order of the phase transition and other phase transition properties varies with the variation of the spatial dimensionality D. The problem for the experimental confirmation of the theoretical predictions about the order of the phase transitions in gauge systems is discussed.