 99118 Janusz Jedrzejewski, Jacek Miekisz
 Ground states of lattice gases with ``almost'' convex repulsive interactions
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Apr 16, 99

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Abstract. To our best knowledge there is only one example of a lattice system
with longrange twobody interactions whose ground states have been
determined exactly: the onedimensional lattice gas with purely
repulsive and strictly convex interactions. Its groundstate
particle configurations do not depend on the rate of decay
of the interactions and are known as the generalized Wigner lattices
or the most homogenenous particle configurations.
The question of stability of this beautiful and universal result
against certain perturbations of the repulsive and convex interactions
seems to be interesting by itself. Additional motivations for studying
such perturbations come from surface physics (adsorbtion on crystal
surfaces) and theories of correlated fermion systems (recent results on
groundstate particle configurations of the onedimensional
spinless FalicovKimball model).
As a first step we have studied a onedimensional lattice gas whose
twobody interactions are repulsive and strictly convex only from
distance 2 on while its value at distance 1 is fixed near its value
at infinity. We show that such a modification makes the groundstate
particle configurations sensitive to the decay rate of the interactions:
if it is fast enough, then particles form $2$particle latticeconnected
aggregates that are distributed in the most homogeneous way.
Consequently, despite breaking of the convexity property, the ground
state exibits the feature known as the complete devil's staircase.
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