Reentrant phase diagram for granular superconductors

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Abstract
The mean-field phase diagram of the self-charging model of a granular superconductor is calculated using the functional-integral formulation. A pronounced reentrance is obtained in quantitative agreement with a previous calculation, involving 2π-antiperiodic eigenstates of the Mathieu equation. It is argued that low-lying, odd-electron-number excitations play a significant role in the thermodynamics of Josephson-junction arrays, for which the Feynman functional-integral formulation holds.