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 to tal interaction of the form V(r)=J/r(2)+Acos(2k(F)ar+phi)/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 phi are the model parameters, whe reas k(F) stands for the wave vector of electrons at the Fermi surface and a is a lattice constant. We search for the (periodic) ground stat es. To solve this difficult problem we have applied an interesting num erical method to accelerate the convergence of Fourier series. A compe tition between dipole-dipole and indirect interactions turns out to be very important. We have found that the reduced chemical potential mu/ J versus A/J phase diagrams contain a region 0.1 less than or equal to A/J less than or equal to 1.5 dominated by only several phases with p eriods up to nine lattice constants. Of course, the resulting sequence of phases (for fixed A/J) depends on the wave vector k(F) and the pha se shift phi. The remaining phase diagram reveals a complex structure of usually long periodic phases. We conjecture, based on the above res ults, that quasi-one-dimensional surface states might be responsible f or experimentally observed ordered phases at the (112) surface of tung sten and molybdenum.