  We propose a lattice gas model to account for linear chain structures
adsorbed on (112) faces of W and Mo. The model includes a dipole-dipole
interaction as well as a long-ranged indirect interaction. We have explicitly
demonstrated that the periodic ground states depend on a competition between
dipole-dipole and indirect interaction. The effect of temperature is studied
within the molecular-field approximation. The numerical results show that for
dipole-dipole interaction only, all long periodic linear chain phases are
suppressed to low temperatures. However, when the long-range indirect
interaction becomes important, the long-periodic linear chain phases start to
fill up the phase diagram and develop a high thermal stability. Model
parameters are chosen to reconstruct a sequence of long-periodic phases as
observed experimentally for Li/Mo(112) and Li/W(112).
