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

Abstract

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

Monte Carlo study of linear chain submonolayer structures. Application to Li/W(112)

“…One possible solution of such problem is accounting for infinite range of indirect interaction. It can be carried out by employing a numerical method to accelerate the convergence of a Fourier series [25] in the same way as in earlier paper [11]. On the other hand it would be interesting to extend an analysis of modulated phases generated by truncation of indirect interaction.…”

“…Preliminary studies performed in molecular field approximation confirmed that competition of dipoledipole interaction and indirect interaction leads to formation of linear chain structures. Further extensive analysis of ground states in related effective one-dimensional model with infinite range of interactions 11 pointed out that competition between these two interactions is crucial in formation of linear chain structures. In very recent investigation of phase transitions in Li/Mo(112) and Sr/Mo(112), H. Pfnür et al 7,12,13 have shown that the lattice gas model could be useful in description of long periodic phases observed at low coverages.…”

Energetics of holmium adsorption on Mo(1 1 2) surface

“…To do this it is convenient to use the grand canonical ensemble (GCE) similarly as for lattice gas model [9,27]. The energy of the configuration per substrate unit cell can be written in GCE as E = Â(− E b − ), where minus E b is energy of the configuration per Ho atom and is the chemical potential.…”

“…Most of the alkaline and alkaline-earth elements form long-periodic chain structures at low coverages. It has been shown [8][9][10][11] that the formation of linear chain submonolayer structures might be due to the competing (repulsive) dipole-dipole interaction and the long-range (oscillatory) indirect interaction between adatoms through the substrate electrons. In the case of adsorption of rare earths metals on the Mo(1 1 2) or W(1 1 2) chain structures are rarely observed [4,6,7].…”

Depinning transitions between adsorbate chains coupled by Friedel oscillations

“…7. The ratio A/Fϭ0.2 used here stems from an optimization 17,18 to describe and simulate the stable phases of this system in the framework of lattice gas models and can be taken as a first approach to the real value. k F in this figure was chosen so that minima appear both at the distances of five and eight lattice constants.…”