Journal of Statistical Physics, Vol. 66, Nos. 1/2, 1992 Phase Diagram of a Random Tiling Quasicrystal

We study the phase diagram of a two-dimensional random tiling model for quasicrystals. At proper concentrations the model has 8-fold rotational sym-metry. Landau theory correctly gives most of the qualitative features of the phase diagram, which is in turn studied in detail numerically using a transfer matrix approach. We find that the system can enter the quasicrystal phase from many other crystalline and incommensurate phases through first-order or continuous transitions. Exact solutions are given in all phases except for the quasicrystal phase, and for the phase boundaries between them. We calculate numerically the phason elastic const~mts and entropy density, and confirm that the entropy density reaches its maximum at the point where phason strains are zero and the system possesses 8-fold rotational symmetry. In addition to the obvious application to quasicrystals, this study generalizes certain surface roughening models to two-dimensional surfaces in four dimensions. KEY WORDS: Quasicrystals; random tiling models; phase diagram; domain walls; incommensurate phases; Landau theory; multicritical points; Hubbard model