THE GLOBAL MINIMUM OF ENERGY IS NOT ALWAYS A SUM OF LOCAL MINIMA - A NOTE ON FRUSTRATION

A classical lattice gas model with translation-invariant, finite-range competing interactions, for which there does not exist an equivalent translation-invariant, finite-range nonfrustrated potential, is constr ucted. The construction uses the structure of nonperiodic ground-state configurations of the model. In fact, the model does not have any per iodic ground-state configurations. However, its ground-state-a transla tion-invariant probability measure supported by ground-state configura tions-is unique.