Glass Transitions and Frustrated Tiling Models

"Tiling models" were originally introduced in an effort to explain low-temperature behavior of glass-forming materials. These models have now been extended by inclusion of "frustration" interactions that limit tile sizes, motivated by observed temperature dependence of supercooled liquid viscosities. The fundamental combinatorial problem presented by tiling-model equilibrium statistical mechanics is discussed in detail, and a simple approximate solution is proposed. The corresponding phase transition behavior is examined, with emphasis on essential singularities at first-order condensation points.