| Abstract: | The equilibrium properties of of a tiling model based on the aperiodic set of Wang tiles by Kari & Culik are investigated. It is found that the transition from the quasiperiodic ground state to the high temperature disordered phase proceeds through periodic phases with first order transitions. We argue that the equilibrium configuration is a consequence of competing length scales and that the model can generally be categorized within the class of models with spatially modulated structures, such as the Frenkel Kontorova and ANNNI models. In contrast to the ANNNI and most similar models, this model exhibits an incommensurate ground state, while commensurate phases occur at higher temperatures, their periods decreasing with increasing temperature." |
