Devil's staircase for nonconvex interactions

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 ene rgy 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-dime nsional problems to one-dimensional ones. The interaction energy in each di rection is assumed here to be repulsive and strictly convex only from dista nce 2 on, while its value at distance 1 can be positive or negative, but cl ose to zero. We show that if the decay rate of the interactions is fast eno ugh, then particles form 2-particle lattice-connected aggregates (dimers) w hich are distributed in the same most homogeneous way as particles whose in teraction is strictly convex everywhere. Moreover, despite the lack of conv exity, the density of particles vs. the chemical potential appears to be a fractal curve known as the complete devil's staircase.