A transfer-matrix Monte Carlo study of random Penrose tilings

Abstract. We investigate the entropic properties of a simple two-dimensional random quasicrystal model: a random tiling by the 36'and 72'rhombi. Applying the transfer matrix Monte Carla (TMMC) method to random tilings for the first time, we have calculated the entropy as a function of phasan strain. We confirm earlier results that the slate of zero phasan strain (i.e. ten-fold symmetry) has the largest entropy; the entropy is 0.4810 ( 5 ) per tile. In addition, by fitting the dependence ofthe entropy on the pharon strain wedetermined 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