Repositório RCAAP

Monte Carlo simulations have begun to illuminate the nature of phase transitions and universality classes for compressible Ising models. A comprehensive analysis of a Landau-Ginsburg Wilson hamiltonian for systems with elastic degrees of freedom predicts that there should be four cases with different behavior, depending upon symmetries and thermodynamic constraints. We shall describe the results of careful Monte Carlo simulations for a simple compressible Ising model that can be easily modified to correspond to each of the four cases.

Monte Carlo simulation has been used to determine the phase diagram of a metamagnet Ising model in the presence of a random and uniform magnetic field. The model consists of a spin-1/2 metamagnet in which the nearest neighbor and next nearest neighbor spin interactions are antiferromagnetic (J1 < 0) and ferromagnetic (J2 > 0), respectively. We used a bimodal probability distribution for the random magnetic field. We have calculated the staggered magnetization and the fourth-order Binder cumulants in order to obtain the critical points. The phase diagram in the uniform field versus temperature plane presents continuous and first-order transition lines. The phase transition lines, together with the critical and tricritical points, have been obtained for several random field values.

Three-dimensional N-vector spin models may define universality classes for such diverse phenomena as i) the superfluid transition in liquid helium (currently investigated in the micro-gravity environment of the Space Shuttle) and ii) the transition from hadronic matter to a quark-gluon plasma, studied in heavy-ion collisions at the laboratories of Brookhaven and CERN. The models have been extensively studied both by field-theoretical and by statistical mechanical methods, including Monte Carlo simulations using cluster algorithms. These algorithms are applicable also in the presence of a magnetic field. Key quantities for the description of the transitions above - such as universal critical amplitude ratios and the location of the so-called pseudo-critical line - can be obtained from the models' magnetic equation of state, which relates magnetization, external magnetic field and temperature. Here we present an improved parametrization for the equation of state of the models, allowing a better fit to the numerical data. Our proposed form is inspired by perturbation theory, with coefficients determined nonperturbatively from fits to the data.

We investigate the equilibrium magnetic properties of a simple cubic small ferromagnetic particle under an external magnetic field. Although the particle is small, it can not be considered as a single-domain unit. The magnetic moments are represented by unitary spin vectors and we consider ferromagnetic interactions between nearest-neighbor spins. The coupling between spins is given in terms of the classical Heisenberg Hamiltonian and we also include a Zeeman contribution and a single-ion uniaxial anisotropy. The size of the particle changes from one to twelve lattice spacings. We employ in our study mean-filed calculations and Monte Carlo simulations. The magnetization and susceptibility curves as a function of temperature show that an uniaxial anisotropy can mimic a ferromagnetic or an antiferromagnetic coupling, depending on the angle between the external magnetic field and the easy axis.

We present results of our numerical study of the critical dynamics of percolation observables for the two-dimensional Ising model. We consider the (Monte Carlo) short-time evolution of the system with small initial magnetization and heat-bath dynamics. We find qualitatively different dynamic behaviors for the magnetization M and for omega, the so-called strength of the percolating cluster, which is the order parameter of the percolation transition. More precisely, we obtain a (leading) exponential form for omega as a function of the Monte Carlo time t, to be compared with the power-law increase encountered for M at short times. Our results suggest that, although the descriptions in terms of magnetic or percolation order parameters may be equivalent in the equilibrium regime, greater care must be taken to interpret percolation observables at short times.

We investigate the critical properties of the spin-3/2 Blume-Capel model in two dimensions on a random lattice with quenched connectivity disorder. The disordered system is simulated by applying the cluster hybrid Monte Carlo update algorithm and re-weighting techniques. We calculate the critical temperature as well as the critical point exponents gamma/<FONT FACE=Symbol>n, b</FONT>/<FONT FACE=Symbol>n, a</FONT>/nu, and nu. We find that, contrary of what happens to the spin-1/2 case, this random system does not belong to the same universality class as the regular two-dimensional ferromagnetic model.

The critical scaling behavior of Ising models with long range interactions is studied. These long-range interactions, when imposed in addition to interactions on a regular lattice, lead to small world graphs. Large-scale Monte Carlo simulations, together with finite-size scaling, is used to obtain the critical behavior of a number of different models. These include the z-model introduced by Scalettar, standard small-world bonds superimposed on a square lattice, and physical small-world bonds superimposed on a square lattice. These scaling results provide further evidence to support the existence of physical (quasi-) small-world nanomaterials.

In this work we study the thermodynamic properties of ultrathin ferromagnetic dots using Monte Carlo simulations. We investigate the vortex density as a function of the temperature and the vortex structure in monolayer dots with perpendicular anisotropy and long-range dipole interaction. The interplay between these two terms in the hamiltonian leads to an interesting behavior of the thermodynamic quantities as well as the vortex density.

Several papers have been written on the complex problem of the stochastic dynamics of the magnetic moments of super-paramagnetic particles, simultaneously with the stochastic rotation of these colloidal particles in a ferrofluid [1-3]. None of these works, however, is sufficiently general and conveniently simple and clear to be used in sumulational works to appropriately describe the experimental super-paramagntetic resonance lines. We have a new proposal for the equations of rotational motion, which is appropriate for simulations. Those equations are stochastic differential equations with multiplicative noise. Therefore, they have to be interpreted as Stratonovich-Langevin equations and the roles of stochastic calculus have to be used in the simulations. For this reason we will briefly present the essence of the numerical algorithms used in the solutions of Stratonovich equations. Finally, the simulational results for the magnetic response functions, and the corresponding dynamic susceptibilities, will be shown and their consequences will be analyzed.

Using molecular dynamics simulation (MD) we have investigated the melting of the two-dimensional Wigner crystal on 240Å-500Å liquid helium films supported by substrates of dielectric constants epsilons = 2.2-7.3. Our results show good agreement with available theoretical and experimental results for densities below 1.0×10(10)cm-2. For higher densities, we notice some disagreements suggesting that quantum effects are important in this regime of densities.

We apply the recently devised quasi-stationary simulation method to study the lifetime and order parameter of the contact process in the subcritical phase. This phase is not accessible to other methods because virtually all realizations of the process fall into the absorbing state before the quasi-stationary regime is attained. With relatively modest simulations, the method yields an estimate of the critical exponent nu|| with a precision of 0.5%.

In this work, we present a new procedure, called sub-sampling, to obtain data concerning time of failure in trials without replacement, (NRT). With this data it is possible to determine the prediction interval (PI) for the future number of failures. We also present an alternative way to evaluate the coverage probability of the prediction interval (PI). The results presented show that the method proposed is reliable and can be useful for the statistical analyses of quality control of processes.

The chaotic low energy region (chaotic sea) of the Fermi-Ulam accelerator model is discussed within a scaling framework near the integrable to non-integrable transition. Scaling results for the average quantities (velocity, roughness, energy etc.) of the simplified version of the model are reviewed and it is shown that, for small oscillation amplitude of the moving wall, they can be described by scaling functions with the same characteristic exponents. New numerical results for the complete model are presented. The chaotic sea is also characterized by its Lyapunov exponents.

These notes give examples of how suitably defined geometrical objects encode in their fractal structure thermal critical behavior. The emphasis is on the two-dimensional Potts model for which two types of spin clusters can be defined. Whereas the Fortuin-Kasteleyn clusters describe the standard critical behavior, the geometrical clusters describe the tricritical behavior that arises when including vacant sites in the pure Potts model. Other phase transitions that allow for a geometrical description discussed in these notes include the superfluid phase transition and Bose-Einstein condensation.

Using variational and diffusion Monte Carlo methods, we have calculated the ground state energy of spinless charged particles (for N < 10) interacting through a repulsive Coulomb potential, moving in two-dimensions and kept together by an external parabolic potential. Using a very simple trial wave function, we obtain results comparable to those of a sophisticated model of a quantum dot.

Voter and Chen version of an Embedded Atom Model has been applied to study the locally stable structures, energies, melting, isomerization and growth patterns of small aluminum clusters, Al n, in the size range of n = 2 - 13. Using molecular dynamics and thermal quenching simulations, the global minima and the other locally stable structures have been distinguished from those stationary structures that correspond to saddle points of the potential energy surface. A large number (10000) of independent initial configurations generated at high temperatures has been used to obtain the stable isomers, and the probabilities of sampling different basins of attractions, for each size of the clusters. Their energy spectra have been determined and melting, and isomerization dynamics are investigated.

A quasiclassical and micro-canonical molecular dynamic simulation techniques have been applied for D2(v, j) + Ni-surface collision systems. Dissociative adsorptions of a D2 molecule on the rigid low index (100), (110) and (111), surfaces of the nickel are investigated to understand the effects of the different surfaces, impact sites and the initial rovibrational states of the molecule on molecule-surface collisions. Interactions between the molecule and the Ni surfaces are mimicked by a LEPS potential. Dissociative chemisorption probabilities of the D2(v, j) Molecule ( for the vibrational (v) = 0 and rotational (j) = 0,1, 3, 10, and for the v = 1, j = 0 states on different impact sites of the surfaces) are presented for the translation energies between 0.001 and 1.0 eV. The probabilities obtained at each collision site have unique behavior for the colliding molecule which is moving along the surface normal direction. It has been observed that at the low collision energies the indirect processes (steering effects) enhance the reactivity on the surfaces. The results are compared to the related studies in the literature.

The cross sections of D2(v,j)+Ni n(T), n = 19 and 20, collision systems have been estimated by using Artificial Neural Networks (ANNs). For training, previously determined cross section values via molecular dynamics simulation have been used. The performance of the ANNs for predicting any quantities in molecule-cluster interaction has been investigated. Effects of the temperature of the clusters and the rovibrational states of the molecule are analyzed. The results are in good agreement with previous studies.

We present Monte Carlo simulations of the lattice gas with nearest-neighbor exclusion and Kawasaki (hopping) dynamics (hard square lattice gas), under the influence of a nonuniform drive, on the square lattice. The drive, which favors motion along the +x axis and inhibits motion in the opposite direction, varies linearly in the y direction. Our lattice has rigid walls at the end points in the y direction and periodic boundaries along the drive. We find that this model has transition to a sublattice-ordered phase at a density of about 0.298, lower than in equilibrium (rhoc <FONT FACE=Symbol>@</FONT> 0.37), but somewhat higher than in the uniformly driven case at maximal bias (rhoc <FONT FACE=Symbol>@</FONT> 0.272). For smaller global densities (r < 0.33), the ordering occurs with particle accumulation in the low-drive region. Above this density we observe a surprising reversal in the density profile, with particles migrating to the high-drive region.

In this work we present a molecular dynamics simulation of a FFM experiment. The tip-sample interaction is studied by varying the normal force in the tip and the temperature of the surface. The friction force, cA, at zero load and the friction coefficient, m, were obtained. Our results strongly support the idea that the effective contact area, A, decreases with increasing temperature and the friction coefficient presents a clear signature of the premelting process of the surface.