Orbital-free density-functional theory for metal slabs.

Orbital-Free Density-Functional Theory (OF-DFT) is known to represent a promising alternative to the standard Kohn-Sham (KS) DFT, as it relies on the electron density alone, without the need to calculate all KS single-particle orbitals and energies. Here, we investigate the behavior of the main ingredients of this theory, which are the non-interacting kinetic-energy density (KED) and the Pauli potential, for metal slabs. We derive explicit density functionals for these quantities in the quantum limit where all electrons are in the same slab discrete level of energy, and we present numerical calculations beyond this quantum limit for slabs of various widths. We have found the first explicit KED functional for a realistic many-particle fermionic system, which we prove to be generally valid with no assumption about the KS potential. We also discuss the total non-interacting kinetic energy and the corresponding enhancement factor, which represent basic quantities for the practical implementation of OF-DFT.

Size effects in finite systems with long-range interactions.

Small systems consisting of particles interacting with long-range potentials exhibit enormous size effects. The Tsallis conjecture [Tsallis, Fractals 3, 541 (1995)FRACEG0218-348X10.1142/S0218348X95000473], valid for translationally invariant systems with long-range interactions, states a well-known scaling relating different sizes. Here we propose to generalize this conjecture to systems with this symmetry broken, by adjusting one parameter that determines an effective distance to compute the strength of the interaction. We apply this proposal to the one-dimensional Ising model with ferromagnetic interactions that decay as 1/r^{1+σ} in the region where the model has a finite critical temperature. We demonstrate the convenience of using this generalization to study finite-size effects, and we compare this approach with the finite-size scaling theory.

Phase transitions and multicritical behavior in the Ising model with dipolar interactions.

In this work, the phase diagram of the ferromagnetic Ising model with dipole interactions is revisited with the aim of determining the nature of the phase transition between stripe-ordered phases with width n (h_{n}) and tetragonal liquid (TL) phases. Extensive Monte Carlo simulations are performed in order to study the short-time dynamic behavior of the observables for selected values of the ratio between the ferromagnetic exchange and dipolar constants δ. The obtained results indicate that the h_{1}-TL phase transition line is continuous up to δ=1.2585, while for the h_{2}-TL line a weak first-order character is found in the interval 1.2585≤δ≤1.36 and becomes continuous for 1.37≤δ≤1.9. This result suggests the existence of a tricritical point close to δ=1.37. When it is appropriate, the complete set of critical exponents is obtained, and in all the studied cases they depend on δ but do not belong to the Ising universality class. Furthermore, short-time dynamic studies reveal that at the point where the mentioned lines meet the h_{1}-h_{2} line, i.e., at δ=1.2585, the critical phase corresponding to the h_{1}-TL transition coexists with the h_{2} phase.

Phase transitions and critical phenomena in the two-dimensional Ising model with dipole interactions: A short-time dynamics study.

The ferromagnetic Ising model with antiferromagnetic dipole interactions is investigated by means of Monte Carlo simulations, focusing on the characterization of the phase transitions between the tetragonal liquid and stripe of width h phases. The dynamic evolution of the physical observables is analyzed within the short-time regime for 0.5≤δ≤1.3, where δ is the ratio between the short-range exchange and the long-range dipole interaction constants. The obtained results for the interval 0.5≤δ≤1.2 indicate that the phase transition line between the h=1 stripe and tetragonal liquid phases is continuous. This finding contributes to clarifying the controversy about the order of this transition. This controversy arises from the difficulties introduced in the simulations due to the presence of long-range dipole interactions, such as an important increase in the simulation times that limits the system size used, strong finite size effects, as well as to the existence of multiple metastable states at low temperatures. The study of the short-time dynamics of the model allows us to avoid these hindrances. Moreover, due to the fact that the finite-size effects do not significantly affect the power-law behavior exhibited in the observables within the short-time regime, the results could be attributed to those corresponding to the thermodynamic limit. As a consequence of this, a careful characterization of the critical behavior for the whole transition line is performed by giving the complete set of critical exponents.

Kohn-Sham exchange potential for a metallic surface.

The behavior of the surface barrier that forms at the metal-vacuum interface is important for several fields of surface science. Within the density functional theory framework, this surface barrier has two nontrivial components: exchange and correlation. Exact results are provided for the exchange component, for a jellium metal-vacuum interface, in a slab geometry. The Kohn-Sham exact-exchange potential V(x)(z) has been generated by using the optimized effective potential method, through an accurate numerical solution, imposing the correct boundary condition. It has been proved analytically, and confirmed numerically, that V(x)(z--> infinity) --> -e(2)/z; this conclusion is not affected by the inclusion of correlation effects. Also, the exact-exchange potential develops a shoulderlike structure close to the interface, on the vacuum side. The issue of the classical image potential is discussed.

Competitive growth model involving random deposition and random deposition with surface relaxation.

A deposition model that considers a mixture of random deposition with surface relaxation and a pure random deposition is proposed and studied. As the system evolves, random deposition with surface relaxation (pure random deposition) take place with probability p and (1-p), respectively. The discrete (microscopic) approach to the model is studied by means of extensive numerical simulations, while continuous equations are used in order to investigate the mesoscopic properties of the model. A dynamic scaling ansatz for the interface width W(L,t,p) as a function of the lattice side L, the time t and p is formulated and tested. Three exponents, which can be linked to the standard growth exponent of random deposition with surface relaxation by means of a scaling relation, are identified. In the continuous limit, the model can be well described by means of a phenomenological stochastic growth equation with a p-dependent effective surface tension.