CLUSTER APPROACH FOR QUASI-CRYSTALS

We consider a ''cluster picture'' to explain the structure and formati on of quasicrystals. Quasicrystal ordering is attributed to a small se t of low-energy atomic clusters which determine the state of minimum f ree energy. The nature of the ground state as T --> 0, depending upon the clusters and cluster energies, ranges from energetically stable an d unique (as in Penrose tilings), to entropically stable and degenerat e (as in random tilings).