H. Chamati

Second-moment interatomic potential for Al, Ni and Ni–Al alloys, and molecular dynamics application

Abstract We present an interatomic potential for Al, Ni and Ni–Al ordered alloys within the second-moment approximation of the tight-binding theory. The potential was obtained by fitting to the total energy of these materials computed by first-principles augmented-plane-wave calculations as a function of the volume. The scheme was validated by calculating the bulk modulus and the elastic constants of the pure metals and alloys that were found to be in fair agreement with the experimental measurements. In addition, we performed molecular-dynamics simulations and we obtained the thermal expansion coefficient, the temperature dependence of the atomic mean-square displacements and the phonon density of states of the compounds. Despite the simplicity of the model, we found satisfactory agreement with the available experimental data.

Second-moment interatomic potential for gold and its application to molecular-dynamics simulations

We have obtained a new interatomic potential for Au in the framework of the second-moment approximation to the tight-binding model by fitting the total energy of the metal as a function of the volume computed by first-principles calculations. The scheme was validated by calculating the bulk modulus, elastic constants, vacancy formation energy and relaxed surface energies of Au, which were found to be in fair agreement with experiment. We also have performed molecular-dynamics simulations at various temperatures and we have determined the temperature dependence of the lattice constant, mean-square displacements, as well as the phonon density of states and the phonon dispersion curves of the metal. The agreement with the available experimental data is much better than previous works based on the same approximation.

Generalized Mittag–Leffler functions in the theory of finite-size scaling for systems with strong anisotropy and/or long-range interaction

The difficulties arising in the investigation of finite-size scaling in d-dimensional O(n) systems with strong anisotropy and/or long-range interaction, decaying with the interparticle distance r as r−d−σ(0 < σ ≤ 2), are discussed. Some integral representations aiming at the simplification of the investigations are presented for the classical and quantum lattice sums that take place in the theory. Special attention is paid to a more general form allowing to treat both cases on an equal footing and in addition cases with strong anisotropic interactions and different geometries. The analysis is simplified further by expressing this general form in terms of a generalization of the Mittag–Leffler special functions. This turned out to be very useful for the extraction of asymptotic finite-size behaviours of the thermodynamic functions.

Finite-size effects in the spherical model of finite thickness

A detailed analysis of the finite-size effects on the bulk critical behaviour of the d-dimensional mean spherical model confined to a film geometry with finite thickness L is reported. Along the finite direction different kinds of boundary conditions are applied: periodic (p), antiperiodic (a) and free surfaces with Dirichlet (D), Neumann (N) and a combination of Neumann and Dirichlet (ND) on both surfaces. A systematic method for the evaluation of the finite-size corrections to the free energy for the different types of boundary conditions is proposed. The free energy density and the equation for the spherical field are computed for arbitrary d. It is found, for 2 < d < 4, that the singular part of the free energy has the required finite-size scaling form at the bulk critical temperature only for (p) and (a). For the remaining boundary conditions the standard finite-size scaling hypothesis is not valid. At d = 3, the critical amplitude of the singular part of the free energy (related to the so-called Casimir amplitude) is estimated. We obtain Δ(p) = −2ζ(3)/(5π) = −0.153 051..., Δ(a) = 0.274 543... and Δ(ND) = 0.019 22..., implying a fluctuation-induced attraction between the surfaces for (p) and repulsion in the other two cases. For (D) and (N) we find a logarithmic dependence on L.

Berezinskii-Kosterlitz-Thouless transition in two-dimensional lattice gas models

Unita´ CNISM e Dipartimento di Fisica ”A. Volta”, Universit a` di Pavia, via A. Bassi 6, I-27100 Pavia, ITALYWe have considered two classical lattice–gas models, consisting of particles that carry multicomponent mag-netic momenta, and associated with a two–dimensional square lattices; each site can host one particle at most,thus implicitly allowing for hard–core repulsion; the pair interaction, restricted to nearest neighbors, is ferro-magnetic and involves only two components. The case of zero chemical potential has been investigated byGrand–Canonical Monte Carlo simulations; the fluctuating o ccupation numbers now give rise to additionalfluid–like observables in comparison with the usual saturat ed–lattice situation; these were investigated and theirpossible influence on the critical behaviour was discussed. Our results show that the present model supports aBerezinskiiˇ–Kosterlitz–Thouless phase transition with a transition temperature lower than that of the saturatedlattice counterpart due to the presence of “vacancies”; com parisons were also made with similar models studiedin the literature.

CRITICAL BEHAVIOR OF SYSTEMS WITH LONG-RANGE INTERACTION IN RESTRICTED GEOMETRY

The present review is devoted to the problems of finite-size scaling due to the presence of long-range interaction decaying at large distance as 1/rd+σ, σ>0. The attention is focused mainly on the renormalization group results in the framework of -theory for systems with fully finite (block) geometry under periodic boundary conditions. Some bulk critical properties and Monte Carlo results are also reviewed. The role of the cut-off effects as well as their relation with those originating from the long-range interaction is additionally discussed. Special attention is paid to the description of an adequate mathematical technique that allows for the treatment of the long-range and short-range interactions equally. The review concludes with a short discussion of some open problems.

Finite-size scaling investigations in the quantum varphi4-model with long-range interaction

In this paper, we study in detail the critical behaviour of the (n ) quantum 4 -model with long-range interaction decaying with distances r by a power law as r -d - in the large-n limit. The zero-temperature critical behaviour is discussed. Its alteration by finite temperature and/or finite sizes in the space is studied. The scaling behaviours are studied in different regimes depending upon whether the finite temperature or the finite sizes of the system lead. A number of results for the correlation length, critical amplitudes and the finite-size shift, for different dimensionalities between the lower d = 3 /2 critical dimensions, are calculated.

Exact results for some Madelung-type constants in the finite-size scaling theory

A general formula is obtained from which the madelung type constant:

Scaling behavior for finite O ( n ) systems with long-range interaction

C(d|\nu)=\int_0^\infty dx x^{d/2-\nu-1}[(\sum_{l=-\infty}^\infty e^{-xl^2})^d-1-(\frac\pi x)^{d/2}]