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 constructed. The construction uses the structure of nonperiodic ground-state configurations of the model. In fact, the model does not have any periodic ground-state configurations. However, its ground-state -- a translation-invariant probability measure supported by ground-state configurations -- is unique. 13 refs., 6 figs