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.