A transfer-matrix Monte Carlo study of random Penrose tilings

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Abstract
The authors 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 Carlo (TMMC) method to random tilings for the first time, they have calculated the entropy as a function of phason strain. They 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 they determined the three stiffness constants in the phason elasticity, one of which is not measurable by previous approaches. They compare the efficacy of the TMMC method with that of other methods.

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