The quasicrystalline state of matter and the role of quasiperiodicity is discussed. Both energetic and entropic mechanisms may stabilize the quasicrystalline phase. For systems where entropy plays the dominant role, random tiling models are the appropriate description. These are discrete statistical models, but without an underlying lattice. Several, though very few, quasicrystalline random tilings have been solved exactly, in the sense that the free energy has been calculated analytically in the thermodynamic limit. The models have besides a quasicrystalline phase also incommensurate phases of which the rotation symmetry is that of an ordinary crystal. The quasicrystalline phase maximizes the entropy. (C) 1998 Elsevier Science B.V. All rights reserved. [References: 25]
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