We propose a lattice gas model to account for linear chain structures adsorbed on (112) faces of tungsten and molybdenum. This model includes a dipole-dipole interaction as well as a long-range indirect (oscillatory) interaction of the form ∼ cos(2kF r + ϕ)/r, where kF is the wavevector of electrons at the corresponding Fermi surface and ϕ is a phase shift. It is assumed that the structures are stabilized by an attractive indirect interaction along the chains.We have explicitly demonstrated that the periodic ground states strongly depend on a competition between the dipole-dipole and long-range indirect interactions.The effect of temperature in our model of linear chain structures is studied within the molecularfield approximation. The numerical results clearly show that for the dipole-dipole interaction only , all long-periodic linear chain phases are suppressed to low temperatures while phases with periods 2, 3, and 4 dominate the phase diagram. 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.We have chosen model parameters in order to reconstruct a sequence of long-periodic phases (for coverages less than 0.5) as observed experimentally at T = 77K for Li/Mo(112) and Li/W(112). It would be interesting to verify our model and assumptions by checking experimentally the corresponding phase diagrams.

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We consider a lattice gas model with an infinite pairwise nonconvex total interaction of the formThis 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 se- ries. A competition between the dipole-dipole and indirect interactions turnsout 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

A simplified theory of incommensurate phase transitions in anisotropically stressed BaMnF4 is proposed. The equilibrium properties and phase transitions induced by temperature and/or anisotropic stress are analysed in terms of the Landau-Ginzburg theory. A conjecture concerning the phase diagram is presented. The occurrence of critical end points or n=2 component 'renormalised' tricritical points is demonstrated within the renormalisation group approach.