First Order Phase Transition in a Model of Quasicrystals
  We introduce a family of two-dimensional lattice models of quasicrystals, using a range of square hard cores together with a soft interaction based on an aperiodic tiling set. Along a low temperature isotherm we find, by Monte Carlo simulation, a first order phase transition between disordered and quasicrystalline phases. 
David Aristoff and Charles Radin
cond-mat.stat-mech math-ph math.MP