The Role of Frustration Interactions in the Thermal Properties of Tiling Models for Glasses.

To represent the apparent inability of supercooled liquids to form infinite amorphous well-bonded regions, we add frustration interactions to the Stillinger-Weber tiling model. Using a simple approximation to the tiling model entropy, we demonstrate that these frustration interactions, which limit tile sizes, can reduce a first order phase transition to a continuous ``transition'' with a sharply peaked heat capacity. The role of frustration is explained using arguments similar to those that apply to finite size effects in first order phase transitions. When corrections from the virial series are added to the simple approximation to the tiling model entropy, previously unexpected first-order phase transitions appear even when limited frustration is present. Because such phase transitions are due to the constraints on the packings of hard cubes, they are artifacts of the tiling models' restriction to cubic domains and may not reflect the behavior of real glass formers.