  We consider a lattice-gas model with an infinite range pairwise noncovex
interaction. It might be relevant, for example, for adsorption of alkaline
elements on W(112) and Mo(112). We study a competition between the effective
dipole-dipole and indirect interactions. The resulting ground state phase
diagrams are analysed (numerically) in detail. We have found that for some
model parameters the phase diagrams contain a region dominated by several
phases only with periods up to nine lattice constants. The remaining phase
diagrams reveal a complex structure of usually long periodic phases. We also
discuss a possible role of surace states in phase transitions.
