- 99-118 Janusz Jedrzejewski, Jacek Miekisz
- Ground states of lattice gases with ``almost'' convex repulsive interactions
Apr 16, 99
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Abstract. To our best knowledge there is only one example of a lattice system
with long-range two-body interactions whose ground states have been
determined exactly: the one-dimensional lattice gas with purely
repulsive and strictly convex interactions. Its ground-state
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
ground-state particle configurations of the one-dimensional
spinless Falicov-Kimball model).
As a first step we have studied a one-dimensional lattice gas whose
two-body 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 ground-state
particle configurations sensitive to the decay rate of the interactions:
if it is fast enough, then particles form $2$-particle lattice-connected
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.