Random negative-U hubbard model

In the case of superconductors whose electrons attract each other only if they are near certain centers, the question arises of how many such centers are needed to make the ground state superconducting? We shall examine it in the context of a random U Hubbard model. In short, we study the case where U-i is - \U\ and 0 with probability c and 1-c, respectively, on a lattice whose sites are labeled i using the Gorkov decoupling and the coherent potential approximation. We argue that for this model there is a critical concentration co below which the system is not a superconductor.