QUASI-CRYSTALLINE GROUND-STATES WITHOUT MATCHING RULES

A simple, local cluster interaction is presented, which has as (only) ground states perfectly quasicrystalline tilings from a single local i somorphism class. Since these tilings do not allow for any perfect mat ching rules, it is thereby shown that the class of structures which ar e the ground state of some finite range interaction is considerably la rger than previously anticipated. Cluster interactions having a quasic rystalline ground state turn out to be simple and robust, and therefor e provide an attractive explanation for the existence of quasicrystals . A simplified version of our cluster interaction is found to have sup er-tile random tiling ground states. Due to the large size of the supe r-tiles, these random tilings still look perfect on a local scale.