Thermodynamics of a Homogeneous Limit-Periodic System

Limit-periodicity describes structures without translational symmetry but which are the union of infinitely many patterns with translational symmetry on increasing scales. Because of its relative simplicity, the limit-perodic Socolar-Taylor tiling offers an ideal system to probe the physical consequences of this distinct type of order. In this undergraduate thesis, we construct a two-deminsional lattice model that possesses this tiling as its ground state, and investigate its properties through simulation and analysis. We find that during a slow quench from the high temperature, disordered phase, the ground state emerges through an infinite series of phase transitions. These transitions are related through scalings of an effective temperature and interaction energy. The system enters a glass-like state during a rapid quench due to the creation of kinetic barriers resulting from a simultaneous occurance of these transtitions. The diffraction pattern of the system is computed for fully and partially ordered states.