An Ultimate Frustration in Classical Lattice-Gas Models

A classical lattice-gas model is called frustrated if not all of its interactions can attain their minima simultaneously. The antiferromagnetic Ising model on the triangular lattice is a standard example.(1, 29) However, in all such models known so far, one could always find nonfrustrated interactions having the same ground-state configurations. Here we constructed a family of classical lattice-gas models with finite-range, translation-invariant, frustrated interactions and with unique ground-state measures which are not unique ground-state measures of any finite-range, translation-invariant, nonfrustrated interactions.