Tiling models for decagonal quasicrystals with quasiperiodic potentials

We study the thermal equilibrium properties of tiling models for decagonal quasicrystals using Monte Carlo simulations. Two-dimensional (2D) rhombus tilings with a ten-fold quasiperiodic potential are used to model the layers in the decagonal quasicrystals where the potential mimics interlayer interactions from the neighboring layers. When the long wavelength density wave with the ten-fold symmetry is used for the potential, the ground state becomes Penrose tiling. At high temperature, equilibrium configurations are locally similar to the maximal random tiling indicating almost free proliferation of phasons as in the unlocked phason phase. However, their phason-space fluctuations seem to remain finite indicating the long-range quasiperiodic ordering, whereas the logarithmic divergence of phason-space fluctuations is expected in an unlocked phase 2D tiling.