Stabilities and Instabilities in Classical Lattice Gas Models without Periodic Ground States
We present a criterion of the stability of nonperiodic ground states. It plays a role of the Peierls condition in models without periodic ground-state configurations. We discuss lattice gas models with stable and unstable nonperiodic ground states. The crystal problem is an attempt to deduce, within statistical mechanics, periodic order in systems of many interacting particles. Our model with a unique stable nonperiodic ground state constitutes a generic counterexample to that problem.
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