A TRANSFER-MATRIX MONTE-CARLO STUDY OF RANDOM PENROSE TILINGS

We investigate the entropic properties of a simple two-dimensional random quasicrystal model: a random tiling by the 36-degrees and 72-degrees rhombi. Applying the transfer matrix Monte Carlo (TMMC) method to random tilings for the first time, we have calculated the entropy as a function of phason strain. We confirm earlier results that the state of zero phason strain (i.e. ten-fold symmetry) has the largest entropy; the entropy is 0.4810 (5) per tile. In addition, by fitting the dependence of the entropy on the phason strain we determined the three stiffness constants in the phason elasticity, one of which is not measurable by previous approaches. We compare the efficacy of the TMMC method with that of other methods.