The Global Minimum of Energy Is Not Always a Sum of Local Minima - a Note on Frustration

Abstract

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.