10-23U

Here we prove that there are such finite-range lattice-gas models (or equivalent spin ones) on the triangular lattice which, in the space of the interaction parameters and the chemical potential, have a full-dimensional region with a continuum of ground states. This fact is due to the nonlinear dependence of the density of energy on the density of particles and is closely related to the problem of infinitely adaptive structures observed in a large number of compounds and the existence of the quasicrystalline and so-called irregularly ordered structures.