An effective Classical model for dissipative Josephson junction arrays

The study of the properties of 2-dimensional dissipative Josephson junction arrays (JJA) is performed by applying the method of Giachetti and Tognetti and Feynman and Kleinert to derive an effective classical action. By this means it is possible to study the effect of ohmic dissipation on the Kosterlitz-Thouless-Berezinskii (KTB) transition which is believed to be responsible (at finite temperatures) for the onset of the phase coherence in the array. The employed method allows the calculation of the effective classical coupling constant and of the phase diagram which exhibits re-entrant behaviour under suitable conditions.