Equilibrium behavior of the tiling model.

Equilibrium properties of the tiling mode, recently introduced by Stillinger and Weber as a means of studying glass phenomena, are investigated. In the two dimensional model, a square lattice is covered by tiles of all sizes. The tiles represent domains of well-packed particles and the boundaries between the domains have a positive mismatch energy proportional to the length of the wall. We have proved that the model has a well defined thermodynamic limit as the size of the system approaches infinity. We have shown how to obtain bounds for the free energy and the transition temperature from the free energy of semi-infinite strips. A transfer matrix method is developed to calculate the free energy of such strips.