Douglas F. de Albuquerque

Critical properties of the classical XY and classical Heisenberg models: A renormalization group study

By using two approaches of renormalization group (RG), mean field RG (MFRG) and effective field RG (EFRG), we study the critical properties of the simple cubic lattice classical XY and classical Heisenberg models. The methods are illustrated by employing its simplest approximation version in which small clusters with one (N′ = 1) and two (N = 2) spins are used. The thermal and magnetic critical exponents, Yt and Yh, and the critical parameter Kc are numerically obtained and are compared with more accurate methods (Monte Carlo, series expansion and e-expansion). The results presented in this work are in excellent agreement with these sophisticated methods. We have also shown that the exponent Yh does not depend on the symmetry n of the Hamiltonian, hence the criteria of universality for this exponent is only a function of the dimension d.

A unified effective‐field renormalization‐group framework approach for the quenched diluted Ising models

A unified effective‐field renormalization‐group framework (EFRG) for both quenched bond‐ and site‐diluted Ising models is herein developed by extending recent works. The method, as in the previous works, follows up the same strategy of the mean‐field renormalization‐group scheme (MFRG), and is achieved by introducing an alternative way for constructing classical effective‐field equations of state, based on rigorous Ising spin identities. The concentration dependence of the critical temperature, Tc(p), and the critical concentrations of magnetic atoms, pc, at which the transition temperature goes to zero, are evaluated for several two‐ and three‐dimensional lattice structures. The obtained values of Tc and pc and the resulting phase diagrams for both bond and site cases are much more accurate than those estimated by the standard MFRG approach. Although preserving the same level of simplicity as the MFRG, it is shown that the present EFRG method, even by considering its simplest size‐cluster version, provid...

Remarks on the traversal time in a tunneling process

Abstract We present the calculation of the traversal time of a flux of particles through a rectangular barrier. We do this using the definition of the duration of a collision from the kinetic point of view in which we use only the current velocity concept. Our result leads to a more transparent physical picture of the problem as compared with others presented in the literature.

Tricritical behavior of a Heisenberg model with Dzyaloshinski-Moriya interaction

Abstract The phase diagram of a spin- 1 2 anisotropic Heisenberg model with Dzyaloshinski-Moriya (DM) interaction is studied in the mean-field approximation. It is shown that for the easy direction ( D =D z ; where D is the DM vector coupling) the model exhibits tricritical point (TCP). The TCP is obtained explicitly and the tricritical temperature, T t , is independent of the exchange anisotropy parameter Δ ( Δ =0 and Δ =1, corresponds to the isotropic Heisenberg and Ising models, respectively), while the tricritical parameter, D t , is dependent on Δ. We obtain T t = 2 3 (z−1) and D t ( Δ =0) D t ( Δ =1), where z is the lattice coordinate number.

Study of the Fe-Al alloys in the Ising model for S = 2 spin by employing the effective field theory

In this work, we study the phase diagram of Fe1−qAlq alloys via site diluted spin-2 ferromagnetic Ising model by employing effective field theory. In contrast with previous studies, here, we incorporate in such model the high-spin S = 2 Fe2+ ion. We consider the same kind of the exchange interaction that of the iron-nickel alloys and we obtain an excellent theoretical description of the experimental data of the T–q phase diagram over the entire range of Al concentration q. In particular, the present calculation provides an excellent agreement with the experimental results for both the anomalous region of Al concentration q (i.e., q<0.2) and for the value of q at which the critical temperature Tc(q) vanishes (i.e., q=qc).

Universality in the site-bond-correlated (SBC) Ising model

Abstract The site-bond-correlated (SBC) model is proposed to describe the phase diagram for KNi p Mg 1− p F3. We treat the square and simple cubic lattices by employing the mean field renormalization group (MFRG) scheme. In this approach, two different exchange interactions (denoted as models A and B) are used. As a result, we find an interesting universal relation between the initial slopes Δ ( μ ) ( α =±1) and Δ ( μ ) ( α =0) (μ denoting model A or B). Therefore, it is possible to estimate the exact values of the initial slope for the case of complete correlation.

Spin-glass phase for the diluted site-bond-correlated version

Abstract We study the site-bond-correlated Ising model in the limit of the negative correlation parameter (α), within the mean-field renormalization group scheme. The ferro—paramagnetic and spin-glass critical lines are obtained explicitly, for general coordination number Z . Phase diagrams are presented for Z = 6 and for some values of the parameter α. In this approach, two different exchange interactions (denoted models A and B) are used. In the phase diagrams, for α ≠ 1, a re-entrant phase is found in both models; when α = −1 this phase disappears.

Site-bond-correlated models for the disordered magnets: Application to KNipMg1−pF3 (abstract)

Site-bond-correlated (SBC) dilution picture has been successfully proposed to account for the striking differences experimentally observed by NMR measurements between random diluted magnet KNipMg1−pF3 and the isostructural compound KMnpMg1−pF3 (see for instance Ref. 1, and references therein). In the SBC picture, the coupling between two nearest-neighbors (nn) magnetic atoms is assumed to be dependent upon the random occupancy of the other nn sites. In this article we study the D-vector model disordered in accordance with the SBC picture in a d-dimensional hypercubic lattice within the framework of the mean field renormalization group. The study is based on two different models (denoted by A and B) for the exchange interactions, in which the random occupancy of the other nn sites is measured by means of a phenomenological parameter α. The critical boundaries of the ferromagnetic and the spin-glass phases with the paramagnetic one, are obtained for various values of the parameter α. The study reveals the e...