J. Miekisz, THE GLOBAL MINIMUM OF ENERGY IS NOT ALWAYS A SUM OF LOCAL MINIMA - A NOTE ON FRUSTRATION, Journal of statistical physics, 71(3-4), 1993, pp. 425-434
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.