Ground states of a one-dimensional lattice-gas model with an infinite-range nonconvex interaction. A numerical study.

We consider a lattice gas model with an infinite pairwise nonconvex total interaction of the form V (r) = J r 2 + A cos(2k F ar + φ) r. This one-dimensional interaction might account, for example, for adsorption of alkaline elements on W(112) and Mo(112). The first term describes the effective dipole-dipole interaction while the other one the indirect (oscillatory) interaction; J, A, and φ are the model parameters, whereas k F stands for the wavevector of electrons at the Fermi surface and a is a lattice constant. We search for the (periodic) ground states. To solve this difficult problem we have applied a novel numerical method to accelerate the convergence of Fourier series. A competition between the dipole-dipole and indirect interactions turns out to be very important. We have found that the reduced chemical potential µ/J versus A/J phase diagrams contain a region 0.1 ≤ A/J ≤ 1.5 dominated by several phases only with periods up to nine lattice constants. Of course, the resulting sequence of phases (for fixed A/J) depends on the wavevector k F and the phase shift φ. The remaining phase diagram reveals a complex structure of usually long periodic phases. We conjecture, based on the above 1 results, that quasi-one-dimensional surface states might be responsible for experimentally observed ordered phases at the (112) surface of tungsten and molybdenum.