An Ultimate Frustration in Classical Lattice-Gas Models

ISSN： 0022-4715

Source： Journal of Statistical Physics, Vol.90, Iss.1-2, 1998-01, pp. : 285-300

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Abstract

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.Our ground-state configurations are two-dimensional analogs of one-dimensional, “most homogeneous,”⁽¹³⁾ nonperiodic ground-state configurations of infinite-range, convex, repulsive interactions in models with devil's staircases.Our models are microscopic (toy) models of quasicrystals which cannot be stabilized by matching rules alone; competing interactions are necessary.