Average partition function of an electron in random binary alloy

We compute the average partition function for an electron moving in a random binary alloy system. A coherent state representation variational (CSRV) method is applied to the single-band tight-banding model Hamiltonian. The results are compared with the exact solution in one-dimensional Anderson's model. The partition function goes over smoothly to the Lifshitz tail in the low-temperature limit and to the result of mean-field theory in the high-density limit. This CSRV method gives the exact results in periodic and very-high-density limit and approaches virtual-crystal theory in small-$\beta$ limit.