Abstract
The random tiling of the plane by a set of objects (e.g., rhombi), related by rotational (e.g. tenfold) symmetries, is a paradigm for the formation of quasiperiodic order due to entropy. Such tilings are mapped to a higher-dimensional space where they form hypersurfaces analogous to the interfaces in a solid-on-solid model. The author argues that the fluctuations of the hypersurface should be described by a gradient-squared free energy of entropic origin; this implies quasi-long-range order in d=2. He shows how the random tiling can be decomposed into layers, defines a transfer matrix, and give prescriptions for using this method to determine numerically the stiffness of the gradient free energy.
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