Claudette Cordeiro

Renormalization-group magnetization of a ferrimagnetic Ising system

We employ a real-space renormalization-group (RSRG) approach to study a mixed-spin (spin-12 and spin-1) antiferromagnetic Ising model on the square lattice. The model incorporates next-nearest-neighbor interactions which are relevant to describe ferrimagnetism. We present an RSRG calculation of the spontaneous magnetization and compensation temperatures of the mixed-spin model. The influence of crystal-field and next-nearest-neighbor interactions on compensation temperatures is studied; the important physical ingredient that leads to the presence of these temperatures is the next-nearest-neighbor coupling between spins 12.

Finite-size scaling for first-order transitions: Potts model

The finite-size scaling algorithm based on bulk and surface renormalization of de Oliveira is tesed onq-state Potts models in dimensionsD=2 and 3. Our Monte Carlo data clearly distinguish between first- and second-order phase transitions. Continuous-q analytic calculations performed for small lattices show a clear tendency of the magnetic exponentY=D-β/v to reach a plateau for increasing values ofq, which is consistent with the first-order transition valueY=D. Monte Carlo data confirm this trend.

Heisenberg ferromagnet with Dzyaloshinsky-Moriya interactions: A real space renormalization group approach

We study the anisotropic Heisenberg ferromagnet with anti-symmetric Dzyaloshinsky-Moriya (DM) interactions for arbitrary dimensions. We use a real space renormalization group approach of the Migdal-Kadanoff type in order to obtain the phase diagrams and critical exponents. The effect of the Dzyaloshinsky-Moriya term in the global phase diagram is worked out in detail. Our results suggest that in all dimensions the effect of the DM interaction is to renormalize the parameters of the anisotropic exchange Hamiltonian. Finally we discuss the modification of hyperscaling associated with the zero temperature Heisenberg-like fixed point.

FERRIMAGNETISM IN TWO-DIMENSIONAL MIXED-SPIN ISING MODEL

We investigate the mixed-spin (spin-1/2 and spin-1) antiferromagnetic Ising model in two dimensions through a real-space renormalization group transformation. The model includes nearest and next-nearest neighbor interactions and is suitable to describe ferrimagnetic ordering. We present the finite-temperature phase diagram of the model. The presence of the second-neighbor bonds enlarge the ferrimagnetic phase. Our results do not indicate the existence of a tricritical point, contrary to previous effective-field calculations.

Dynamical behavior of the random-bond transverse Ising model with four-spin interactions

We study the time evolution of the one-dimensional random-bond transverse Ising model with four-spin interactions. We calculate the time-dependent correlation function as well as the longitudinal relaxation function of the infinite chain. We analyze how the presence of disorder affect the dynamical behavior of the system in comparison with the pure model. We find that the main effect of disorder is to produce a crossover from a central mode to a collective-mode type of dynamics, as the concentration of weaker bonds is enhanced. Such crossover is also present in the case of an increase in bond dilution. The role of time evolution of one-dimensional quantum spin systems has been a long-standing theoretical and experimental problem. 1 Among them, the transverse Ising model with multispin interactions, regarded as one of the simplest with a nontrivial dynamics, has attracted considerable interest in recent years. 2,3 On the other hand, the presence of bond randomness has been shown to affect the behavior of magnetic materials in a drastic way providing a very rich area of investigation. In some materials it is present in the form of dilution caused by missing magnetic bonds or sites. In other class of systems it manifests itself through fluctuations in the magnitude of the exchange couplings due to structural disorder, as in glassy materials. Most of the research in disordered systems have been concentrated on obtaining phase diagrams and thermodynamic functions. 3 Much less effort has been made to obtain the dynamical behavior of these systems. Recently, the time evolution of the usual two-body random transverse Ising system was carried out by means of the method of recurrence relations. 4 The crossover from a central

Optical dichroism by nonlinear excitations in graphene nanoribbons

The honeycomb carbon structure of graphene and nanotubes has a dynamics which can give rise to a spectrum. This can be excited via the interaction with an external electromagnetic field. In this work, non-linear waves on graphene and nanotubes associated with the carbon structure are investigated using a gauge model. Typical energies are estimated and there scaling with the nanoribbon width investigated. Furthermore, the soliton-photon interaction depends on the incident photon polarization. In particular, we find that the nanoribbon is transparent when the polarization is along the largest length. Relying on the scaling with the width, we suggest a way to experimentally identify the soliton waves in nanoribbons.

Reconstruction of the free energy in the metastable region using the path ensemble.

By quenching into the metastable region of the three-dimensional Ising model, we investigate the paths that the magnetization (energy) takes as a function of time. We accumulate the magnetization (energy) paths into time-dependent distributions from which we reconstruct the free energy as a function of the magnetic field, temperature, and system size. From the reconstructed free energy, we obtain the free-energy barrier that is associated with the transition from a metastable state to the stable equilibrium state. Although mean-field theory predicts a sharp transition between the metastable and the unstable region where the free-energy barrier is zero, the results for the nearest-neighbor Ising model show that the free-energy barrier does not go to zero.

Quantum spin-12 two-dimensional XXZ model: an alternative quantum renormalization-group approach

We study the phase diagram of the two-dimensional quantum spin-12 anisotropic Heisenberg model. We adapt a renormalization-group approach to treat this quantum model, and an analysis on low temperatures is presented and compared with the exact results in the isotropic limit, obtained from the Mermin–Wagner theorem. We comment on extensions of the procedure to treat antiferromagnetic models, for S=12 and S>12.

Dynamical behavior of the four-body transverse Ising model with random bonds and fields

We study the effect of random bonds and fields on the dynamical behavior of the one-dimensional transverse Ising model with four-spin interactions. We consider finite chains of increasing size to determine the time-dependent correlation function and the longitudinal relaxation function of the infinite chain. In this fully disordered system we observe a crossover from a collective modetype of dynamics to that of a central regime.

The Electronic Behavior of Zinc-Finger Protein Binding Sites in the Context of the DNA Extended Ladder Model

Instead of ATCG letter alignments, typically used in bioinformatics, we propose a new alignment method using the probability distribution function of the bottom of the occupied molecular orbital (BOMO), highest occupied molecular orbital (HOMO) and lowest unoccupied orbital (LUMO). We apply the technique {\color{red} to transcription} factors with Cys2His2 zinc fingers. These {\color{red} transcription} factors search for binding sites, probing for the electronic patterns at the minor and major DNA groves. The eukaryotic Cys2His2 zinc finger proteins bind to DNA ubiquitously at highly conserved domains. They are responsible for gene regulation and the spatial organization of DNA. To study and understand these zinc finger DNA-protein interactions, we use the extended ladder in the DNA model proposed by Zhu, Rasmussen, Balatsky \& Bishop (2007) \cite{Zhu-2007}. Considering one single spinless electron in each nucleotide