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.