The Schrödinger operator for the field generated by the randomly arranged particles with a single-site potential is studied as a model of amorphous materials. If the particles have no interactions, it is well-known that the integrated density of states (IDS) for the Schrödinger operator decays exponentially near its spectral lower edge. In this presentation, I consider the model where the particles have interactions and compare the asymptotic behavior of the IDS of this model with a non-interaction model. In most cases, the effect of interactions on the IDS is weak. However, for a pair-wise interaction model, the effect can be significant.