Theory of superconducting wire networks and Josephson-junction arrays in magnetic fields

In this paper we study the superconducting-normal phase boundaries of a variety of wire networks and Josephson-junction arrays. We have obtained the mean-field phase diagrams for a number of geometries and compared them to the corresponding experimental data. We have introduced an analytical approach to the analysis of the structures present in the phase diagrams. We have shown in great detail how the gross structure is determined by the statistical distributions of the cell areas, and how the fine structures are determined by correlations among neighboring cells in the lattices. We have also studied the effect of thermal fluctuations on the structure of the phase diagram by a cluster mean-field calculation and a real-space renormalization-group (RG) theory. The RG theory provides a natural link between the structures at fractional fluxes to those at integral ones, predicting a pronounced hierarchical behavior of the phase diagram and an infinite slope for the cusps.