We studied a layered mixed-spin Ising model, with spins s = 1/2 and S = 1, distributed on the sites of a hexagonal lattice. For this spin arrangement, any spin at one lattice site has two nearest-neigbor spins of the same type, and four of the other type. We assumed that the exchange interaction between spins s and S is antiferromagnetic, with the value J1. J2 is the exchange interaction between two nearest neighbor s spins, and J3 is the coupling between two nearest neighbor S spins. We also considered a single-ion crystal-field contribution D to the S sites. We performed mean-field calculations and Monte Carlo simulations to determine the compensation point of the model. We have shown that a compensation point can be present for any positive value of D. We have also found a negative lower bound for D, below which a compensation point can not appear. For each value of D, we determined the range of values of the J2 and J3 couplings for which a compensation point is realizable.

In this work we studied a ferromagnetic mixed-spin Ising model including a single ion crystal-field term. The model system consists of two interpenetrating sublattices with spins sigma = 1/2 and S = 1. The spins sigma = 1/2 occupy the sites of one sublattice, their nearest-neighbours are spins S on the other sublattice, and vice versa. The system is in contact with a heat bath, the spins flipping according to the Metropolis transition rate and, at the same time, subject to an external flow of energy, which is simulated by a two-spin flip process. The model is studied via the dynamical pair approximation and through Monte Carlo simulations. We have determined the phase diagram of the model in the plane crystal-field D versus competition parameter p. The parameter p accounts for the competition between the one- and two-spin flip processes. In the pair approximation, the phase diagram, at high temperatures, present three phases separated by two transition lines: a continuous transition line between the ferromagnetic and paramagnetic phases, and a first-order transition line between the paramag-netic and antiferromagnetic phases. However, Monte Carlo simulations predict the same topology for the phase diagram as the pair approximation, but all the transition lines are continuous for any value of the temperature.

In this work we studied the effects of non active sites on the substrate of a growing surface. In our model a particle only sticks at the surface if the site where it falls is an active site. However, we allow the deposited particle to diffuse along the surface in accordance with some previously defined mechanism. Using Monte Carlo simulations, and some analytical results, we have investigated the model in (1+1) and (2+1) dimensions, considering different relaxation mechanisms. We show that the inclusion of non active sites is a crucial point in the model. In fact, we have observed that the saturation regime always disappears and that the values of the growth exponent beta go to one, at large times, for any mechanism of diffusion we considered in one and two dimensions.

Hydrogen bonded liquids like water present a rich thermodynamic behaviour due to the strength and directionality of the bonds. In a recent paper a geometric model based on Bernal's model for liquids was proposed to study the effects of the hydrogen bonds on the phase transitions of water, under pressure and temperature variations. Water molecules were assumed to stay at the vertices of coordination r (r = 4; 5; 6) of perfectly tiled polygons, and to have four links which allow up to four hydrogen bonds per particle. Mean field calculations yielded a phase diagram with three phases of different densities and a critical point at the end of the coexistence line between the high and low density phases. The three phases were considered to be liquids of different densities. In the present work we have shown that applying some geometric constraints to particle arrangements (thus correcting the system entropy, which was overestimated in the previous work), and allowing a variable number of links per molecule, leads to substantial alteration of the phase diagram. Three phases of different densities are still present, but no critical point appears. Two of the phases are solid, and one phase is amorphous.

We studied in this work a competitive reaction model between monomers on a catalyst. The catalyst is represented by hypercubic lattices in d = 1, 2 and 3 dimensions. The model is described by the following reactions: A + A -> A2 and A + B -> AB, where A and B are two monomers that arrive at the surface with probabilities yA and yB, respectively. The model is studied in the adsorption controlled limit where the reaction rate is infinitely larger than the adsorption rate. We employ site and pair mean-field approximations as well as static and dynamical Monte Carlo simulations. We show that, for all d, the model exhibits a continuous phase transition between an active steady state and a B-absorbing state, when the parameter yA is varied through a critical value. Monte Carlo simulations and finite-size scaling analysis near the critical point are used to determine the static critical exponents b,n^ and the dynamical critical exponents n||, d, h and z. The results found for this competitive reaction model are in accordance with the conjecture of Grassberger, which states that any system undergoing a continuous phase transition from an active steady state to a single absorbing state, exhibits the same critical behavior of the directed percolation universality class.

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 flip Glauber dynamics, while the flux 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 have 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.

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 finite size scaling hypothesis, the approximate critical behavior of model on infinite lattice is obtained through the exact computation of some thermal quantities of the model on finite clusters. In this work some of these methods are reviewed, namely the mean field renormalization group, the effective field renormalization group and the finite size scaling renormalization group procedures. Although special emphasis is given to the mean field renormalization group (since it has been, up to now, much more used to study a wide variety of different systems) a discussion of their potentialities and interrelations to other methods is also presented.

A dois anos do centenário da identificação do reflexo cutâneo-plantar em extensão como sinal de afecção do sistema nervoso central, pareceu-nos oportuno traduzir passagens relevantes de Babinski sobre o fenômeno que descreveu. Há indícios de que um dos motosmais influentes na criação do espírito de época que facilitou a valorização clínica do "fenômeno dos artelhos", deveu-se à exigência pragmática de se distinguir paralisias "histéricas" de "orgânicas" para aplicação médico-legal imediata.

The extensor plantar reflex was described by Babinski in 1896. Given the obvious relevance of the sign for internal medicine as well as the paucity of translations of the original sources into Portuguese, we thought it timely to recall the ingenious arguments Babinski used to demonstrate his views on the "toe phenomenon", as he would call it. A careful analysis of Babinski's writings suggests, further, that he was driven by keen intuition as well as by medico-legal interests.