  We study ground-state orderings of particles in classical lattice-gas 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 the two-dimensional problem
to a one-dimensional one. The interaction energy in each direction is 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 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
versus the chemical potential appears to be a fractal curve known as the
complete devil's staircase.
