STABLE QUASI-CRYSTALLINE GROUND-STATES

We give strong evidence that noncrystalline materials such as quasicry stals or incommensurate solids are not exceptions, but rather are gene ric in some regions of phase space. We show this by constructing class ical lattice-gas models with translation-invariant finite-range intera ctions and with a unique quasiperiodic ground state which is stable ag ainst small perturbations of two-body potentials. More generally, we p rovide a criterion for stability of nonperiodic ground states.