Entropy saturation and the Brinkmann-Rice transition in a random-tiling model

The parameter regime in which a Brinkmann-Rice (BR) transition appears near half-filling is investigated for a model of of one kind of electrons traversing a plane randomly tiled with CuO_4 molecules, simulating the copper-oxide planes of high-T_c superconductors. As the hole doping is increased, the BR transition evolves continuously into a state characterized by Kauzmann-like plateaus in the entropy vs. temperature curves. Despite clear analogies with the glass transition, these are equilibrium properties of the model. This is because the spin interactions, responsible for ordering in real space, are not included.