Finite-Temperature Order-Disorder Phase Transition in a Cluster Model of Decagonal Tilings

In a recent paper ["Cluster Model of Decagonal Tilings" (to be published in Phys. Rev. B)], we have introduced a cluster model for decagonal tilings in two dimensions. This model is now extended to three dimensions. Two-dimensional tilings are stacked on top of each other, with a suitable coupling between adjacent layers. An energy model with interactions leading to a perfect decagonal quasicrystal at low temperatures is studied by Monte Carlo simulations. An order parameter is defined, and its dependence on temperature and system size is investigated. Evidence for a finite-temperature order-disorder phase transition is presented. The critical exponents of this transition are determined by finite-size scaling.