Volume 50, Number 3, May I 2000
|Page(s)||307 - 311|
|Published online||01 September 2002|
Devil's staircase for nonconvex interactions
Institute of Theoretical Physics,
University of Wrocław pl. Maksa Borna 9, 50-204 Wrocław, Poland
Department of Theoretical Physics,
University of Łódź ul. Pomorska 149/153, 90-236 Łódź, Poland
2 Institute of Applied Mathematics and Mechanics, University of Warsaw ul. Banacha 2, 02-097 Warszawa, Poland
Corresponding authors: email@example.com firstname.lastname@example.org
Accepted: 25 February 2000
We study rigorously ground-state orderings of particles in one-dimensional classical lattice gases with nonconvex interactions. Such systems serve as models of adsorption on crystal surfaces. In the considered models, the energy of adsorbed particles is a sum of two components, each one representing the energy of a one-dimensional lattice gas with two-body interactions in one of the two orthogonal lattice directions. This feature reduces two-dimensional problems to one-dimensional ones. The interaction energy in each direction is assumed here to be repulsive and strictly convex only from distance 2 on, while its value at distance 1 can be positive or negative, but close to zero. We show that if the decay rate of the interactions is fast enough, then particles form 2-particle lattice-connected aggregates (dimers) which are distributed in the same most homogeneous way as particles whose interaction is strictly convex everywhere. Moreover, despite the lack of convexity, the density of particles vs. the chemical potential appears to be a fractal curve known as the complete devil's staircase.
PACS: 05.50.+q – Lattice theory and statistics / 61.44.Fw – Incommensurate crystals / 68.65.+g – Low-dimensional structures
© EDP Sciences, 2000
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