*Europhys. Lett.*,

**50**(3), pp. 307-311 (2000)

## Devil's staircase for nonconvex interactions

^{1}
Institute of Theoretical Physics,
University of Wrocław pl. Maksa Borna 9, 50-204 Wrocław, Poland
and
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: jjed@ift.uni.wroc.pl miekisz@mimuw.edu.pl

Received:
9
July
1999

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*