Bartira Grandi - Academia.edu (original) (raw)

Papers by Bartira Grandi

Brazilian Journal of Physics, 2000

We study ferromagnetic and antiferromagnetic Ising models in contact with a heat reservoir, and s... more We study ferromagnetic and antiferromagnetic Ising models in contact with a heat reservoir, and subject to an external source of energy. The contact with the heat bath is simulated by a single-spin ip Glauber dynamics, while the ux of energy is simulated by the two-spin exchange Kawasaki process. Pair approximation and Monte Carlo calculations are employed to determine the phase diagram for the stationary states of the model. We report the results we h a ve obtained in one, two and three dimensions. For instance, in one dimension, while the pair approximation predicts a phase transition for the ferromagnetic case, this is not corroborated by the Monte Carlo simulations. We also use Monte Carlo simulations to evaluate the static and dynamic critical exponents at the transition lines between nonequilibrium steady states. We show that the critical exponents agree with those of the corresponding equilibrium Ising model, for which detailed balance is obeyed.

We studied in this work a modified version of the Ziff, Gulari and Barshad (ZGB) model in which t... more We studied in this work a modified version of the Ziff, Gulari and Barshad (ZGB) model in which the adsorption probabilities of CO and O2 are site dependent. We employed Monte Carlo simulations to determine the phase diagram of the model as a function of the partial pressure of CO in the gaseous phase, and of the relative adsorption probabilities. For the case where there is no site with affinity only to O2 adsorption, we found that the non physical O-poisoned state disappears. This feature can not be seen in the usual ZGB model.

Physical Review B, 1994

We study, within the dynamic-pair approximation, the behavior of the antiferromagnetic Ising mode... more We study, within the dynamic-pair approximation, the behavior of the antiferromagnetic Ising model in contact with a heat bath and subject to an external source of energy. The contact with the heat bath is simulated by the Glauber process while the continuous flux of energy into the system is simulated by the Kawasaki process. We find the phase diagram of this model, and we show that, conversely to what happens for the ferromagnetic Ising model, the antiferromagnetic Ising model does not show the phenomenon of self-organization within the dynamic-pair approximation.

Physical Review E, 1997

... Rev. B 50, 12 595 1994 . 2 RJ Glauber, J. Math. Phys. 4, 294 1963 . 3 K. Kawasaki, in Phase T... more ... Rev. B 50, 12 595 1994 . 2 RJ Glauber, J. Math. Phys. 4, 294 1963 . 3 K. Kawasaki, in Phase Transitions and Critical Phenomena, edited by C. Domb and MS Green Academic, London, 1972 , Vol. 4. ? 4 T. Tome and MJ de Oliveira, Phys. Rev. A 40, 6643 1989 . ...

Physica A: Statistical Mechanics and its Applications, 1997

The two-dimensional Ising model in contact with a heat bath at infinite temperature, T → ∞, is co... more The two-dimensional Ising model in contact with a heat bath at infinite temperature, T → ∞, is considered. The model is subject to two competing stochastic processes: the Glauber dynamics with probability p and the Kawasaki one with probability (1 − p). The Glauber process is associated to the random flipping of single spins at T → ∞, while the

Modern Physics Letters B, 1996

We have studied the behavior of the one-dimensional ferromagnetic Ising model in contact with a h... more We have studied the behavior of the one-dimensional ferromagnetic Ising model in contact with a heat bath and subject to an external source of energy. The contact with the heat bath is simulated by a process of Glauber type, while the continuous flux of energy into the system by a process of Kawasaki type. We show, within the dynamical pair approximation that the phase diagram exhibits a line of continuous nonequilibrium transitions between the paramagnetic and antiferromagnetic phases. However, detailed Monte Carlo simulations on the same model show clearly that the only stationary state is the paramagnetic one, whatever is the value of the competition parameter between the Glauber and Kawasaki dynamics.

Physical Review E, 1996

... We think that our model, which exhibits the self-organization phenomenon, due the competition... more ... We think that our model, which exhibits the self-organization phenomenon, due the competition between the Glauber and configuration dependent ... It is a pleasure to thank Mario Jose de Oliveira for the many suggestions and fruitful discussions during the development of this ...

Brazilian Journal of Physics, 1999

Some renormalization group approaches have been proposed during the last few years which are clos... more Some renormalization group approaches have been proposed during the last few years which are close in spirit to the Nightingale phenomenological procedure. In essence, by exploiting the nite size scaling hypothesis, the approximate critical behavior of model on in nite lattice is obtained through the exact computation of some thermal quantities of the model on nite clusters. In this work some of these methods are reviewed, namely the mean eld renormalization group, the e ective eld renormalization group and the nite size scaling renormalization group procedures. Although special emphasis is given to the mean eld renormalization group since it has been, up to now, much more used to study a wide variety of di erent systems a discussion of their potentialities and interrelations to other methods is also presented.

Physical Review E, 1999

We consider a three-dimensional ferromagnetic Ising model on a cubic lattice in contact with a he... more We consider a three-dimensional ferromagnetic Ising model on a cubic lattice in contact with a heat bath at temperature T. The states of the system evolve in time according to two stochastic processes: the one-spin-flip Glauber dynamics where the order parameter is not conserved, and the two-spin-exchange Kawasaki kinetics, which conserves the order parameter. The former process mimics an input of energy into the system. Monte Carlo simulations were employed to determine the phase diagram for the stationary states of the model, and the corresponding critical exponents. Similarly to the observed for the related two-dimensional ferromagnetic Ising model, the phase diagram obtained exhibits the phenomenon of self-organization. Although the stationary states are mainly ferromagnetic at low temperatures, an antiferromagnetic phase appears for extremely high values of the flux of energy. Unlike the ferromagnetic case, the region of the phase diagram occupied by the antiferromagnetic phase is now larger. The determined critical exponents for this nonequilibrium model are in agreement with the well-known accepted values for the three-dimensional equilibrium Ising model.

Physics Letters A

Through the spin-wave theory we have calculated the thermodynamic phase boundary which separates ... more Through the spin-wave theory we have calculated the thermodynamic phase boundary which separates the antzferromagnetlc and spin-flop phases of amsotropzc antfferromagnets. While spin-wave theories predict a mimmum as a function of the temperature for the limzts of stability of both phases, our results show that this mimmum does not appear for the thermodynamic phase boundary. We also show that m the case of singleqon uniaxial anisotropy the thermodynamic field increases wath the temperature according a T 7/2 law

Caderno Brasileiro De Ensino De Fisica, 1988

Physica Status Solidi, 2001

physica status solidi (a), 2001

We performed Monte Carlo simulations to study catalytic surface reaction of the type 1 2 A 2 þ BA... more We performed Monte Carlo simulations to study catalytic surface reaction of the type 1 2 A 2 þ BA ! A 2 B. We chose two different types of catalytic surfaces in our studies: one represented by a square lattice (coordination number four) and the other represented by a triangular lattice (coordination number six). The whole process can be described by a single parameter, which is taken as the relative adsorption of BA molecules. In our model, we always need two nearest neighbor sites to the adsorption of both molecules. After deposition, the A 2 molecules dissociate occupying two nearest neighbor sites, while the BA molecules stay bound. The reaction occurs only when a free A atom is nearest neighbor of a B atom of the BA molecule. In spite of each reaction freeing three empty sites on the lattice, this model does not exhibit any reactive window for both lattices. Only when we introduce processes like the diffusion of BA molecules or free A atoms, or desorption of BA molecules, the catalytic surface can become active for some values of deposition rate y BA. As to be expected, the reactivity over the triangular lattice is higher than that observed on the square lattice.

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 1999

We consider a two-dimensional antiferromagnet Ising system interacting with a heat bath at temper... more We consider a two-dimensional antiferromagnet Ising system interacting with a heat bath at temperature T. The dynamics of the system is simulated by two competing stochastic processes: the two-spin-exchange Kawasaki kinetics at temperature T>0 and the one-spin-flip Glauber dynamics at T(G)-->0(-), which mimics the increase of the energy of the system. These two processes have probabilities 1-p and p, respectively. Monte Carlo simulations were employed to determine the phase diagram for the stationary states of the model and the corresponding critical exponents. Contrary to the ferromagnetic case, the phase diagram obtained does not exhibit the phenomenon of self-organization: for any nonzero value of the competing parameter p, and for any value of T, the only stationary phase which remains is the ferromagnetic one. At the phase transition between the antiferromagnetic and paramagnetic phases, at p=0, the values found for the critical exponents agree with those of the correspon...

Physical Review E, 2002

We study a version of the Ziff-Gulari-Barshad model where we include the diffusion of oxygen atom... more We study a version of the Ziff-Gulari-Barshad model where we include the diffusion of oxygen atoms between the uppermost layer and the subsurface. When a CO molecule impinges the surface, it occupies a single site, while the O2 molecule needs two neighboring sites to be adsorbed. The oxidation of the CO molecule occurs only at the top layer, and this happens whenever a CO molecule is nearest neighbor of an O atom. Through the pair mean-field approximation we determine the phase diagram of the model for different values of the diffusion rate of oxygen atoms between the subsurface and the top layer. The diagram exhibits a continuous line that separates regions displaying O-poisoned and non-O-poisoned states. We show that above a critical value of the diffusion rate of oxygen atoms from the subsurface to the top layer, there is no more oxygen poisoning for any nonzero value of the diffusion rate from the top layer to the subsurface. This behavior is also verified in Monte Carlo simulations.

Physical Review E, 2004

We employed Monte Carlo simulations and short-time dynamic scaling to determine the static and dy... more We employed Monte Carlo simulations and short-time dynamic scaling to determine the static and dynamic critical exponents for the generalized two-dimensional Blume-Capel model of spin-3/2. We showed that the critical behavior at the second-order phase-transition line between the paramagnetic and ferromagnetic phases is in the same universality class of the two-dimensional Ising model. However, at the double critical end point, which is present in the phase diagram of the model, the critical exponent beta , associated to the order parameter, is different from that of the Ising model.

Physical Review B, 2006

We determined the phase diagram of a three-dimensional uniaxial antiferromagnetic particle in the... more We determined the phase diagram of a three-dimensional uniaxial antiferromagnetic particle in the presence of an external magnetic field parallel to its easy axis through Monte Carlo calculations. The structure of the particle is a simple cubic lattice, where its magnetic moments are distributed in spherical shells centered around a given site. The magnetic moments are continuous vectors that interact

physica status solidi (a), 2007

ABSTRACT In this work we study a catalytic reaction model among three monomers in order to unders... more ABSTRACT In this work we study a catalytic reaction model among three monomers in order to understand the chemical kinetics of the selective catalytic reduction of nitrogen oxide by ammonia (4NO + 4NH3 + O2 → 4N2 + 6H2O). Our model takes into account the formation of the intermediate species in the global scheme of the reaction. In order to determine the dynamical behaviour of the model we used single site approximation method. In this approach we have observed that, depending on the values of the control parameters, the model presents an active or an inactive phase. In fact, the dynamical phase diagram of the model exhibits a first order line separating these two phases. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)