  A quantum pseudo-spin model with random spin sizes is introduced to study the
effects of charging-energy disorder on the superconducting transition in
granular superconducting materials. Charging-energy effects result from the
small electrical capacitance of the grains when the Coulomb charging energy is
comparable to the Josephson coupling energy. In the pseudo-spin model,
randomness in the spin size is argued to arise from the inhomogeneous
grain-size distribution. For a particular bimodal spin-size distribution, the
model describes percolating granular superconductors. A mean-field theory is
developed to obtain the phase diagram as a function of temperature, average
charging energy and disorder.
