AN ULTIMATE FRUSTRATION IN CLASSICAL LATTICE-GAS MODELS

A classical lattice-eas model is called frustrated if not all of its i nteractions can attain their minima simultaneously. The antiferromagne tic Ising model on the triangular lattice is a standard example.((1,29 )) However, in all such models known so far, one could always find non frustrated interactions having the same ground-state configurations. H ere we constructed a family of classical lattice-gas models with finit e-range, translation-invariant, frustrated interactions and with uniqu e ground-state measures which are not unique ground-state measures oi any finite-range, translation-invariant, nonfrustrated interactions. O ur ground-state configurations are two-dimensional analogs of one-dime nsional, ''most homogeneous,''((13)) nonperiodic ground-state configur ations of infinite-range, convex, repulsive interactions in models wit h devil's staircases. Our models are microscopic (toy) models of quasi crystals which cannot be stabilized by matching rules alone; competing interactions are necessary.