Statistical Mechanics of Random Tiling Quasicrystals

This thesis studies analytically and numerically the statistical mechanical properties of two-dimensional random tiling quasicrystals. We focus on a particular model of quasicrystals that is able to exhibit 8-fold symmetric diffraction patterns. This system is well described by two sets of interacting domain walls running in two different directions and contains crystal phases, incommensurate phases and quasicrystal phases. We study phase transitions among these phases and find first order transitions as well as commensurate-incommensurate transitions. The phase diagram of this model is explored and various cross sections are presented.