Rigorous Bound on the Integrated Density of States of a Three-Dimensional Random Alloy

We study the lattice model of a random alloy whose Hamiltonian is H=−Σr,δt a†rar+δ + Σrεra†rar, where δ are nearest-neighbor vectors and εr is a random site-diagonal energy uniformly distributed over the interval 0≤εr≤W. We prove that the integrated density of states per site N−1Z(E) satisfies the inequality, N−1Z(E)≤C1e−C2/E, where C1 and C2 are constants.