Anna Chame

Dewetting of a Solid Monolayer

We report on the dewetting of a monolayer on a solid substrate, where mass transport occurs via surface diffusion. For a wide range of parameters, a labyrinthine pattern of bilayer islands is formed. An irreversible regime and a thermodynamic regime are identified. In both regimes, the velocity of a dewetting front, the wavelength of the bilayer island pattern, and the rate of nucleation of dewetted zones are obtained. We also point out the existence of a scaling behavior, which is analyzed by means of a geometrical model.

Crossover effects in a discrete deposition model with Kardar-Parisi-Zhang scaling.

We simulated a growth model in (1+1) dimensions in which particles are aggregated according to the rules of ballistic deposition with probability p or according to the rules of random deposition with surface relaxation (Family model) with probability 1-p. For any p>0, this system is in the Kardar-Parisi-Zhang (KPZ) universality class, but it presents a slow crossover from the Edwards-Wilkinson class (EW) for small p. From the scaling of the growth velocity, the parameter p is connected to the coefficient lambda of the nonlinear term of the KPZ equation, giving lambda approximately p(gamma), with gamma=2.1+/-0.2. Our numerical results confirm the interface width scaling in the growth regime as W approximately lambda(beta)t(beta) and the scaling of the saturation time as tau approximately lambda(-1)L(z), with the expected exponents beta=1/3 and z=3/2, and strong corrections to scaling for small lambda. This picture is consistent with a crossover time from EW to KPZ growth in the form t(c) approximately lambda(-4) approximately p(-8), in agreement with scaling theories and renormalization group analysis. Some consequences of the slow crossover in this problem are discussed and may help investigations of more complex models.

Dewetting of solid films with substrate-mediated evaporation.

The dewetting dynamics of an ultrathin film is studied in the presence of evaporation-or reaction-of adatoms on the substrate. KMC simulations are in good agreement with an analytical model with diffusion, rim facetting, and substrate sublimation. As sublimation is increased, we find a transition from the usual dewetting regime where the front slows down with time, to a sublimation-controlled regime where the front velocity is approximately constant. The rim width exhibits an unexpected nonmonotonous behavior, with a maximum in time.

Irreversible processes: The generalized affinities within Tsallis statistics

Within the generalized statistical mechanics introduced recently by Tsallis, the generalized form of the affinities (the quantities which drive a process in the theory of irreversible thermodynamics) was derived. The affinities were obtained by considering changes in the generalized entropy SqAUB of a system composed by two subsystems A and B. The non-extensive character of the Tsallis entropy is taken into account. At the end, the equilibrium condition is discussed and the zeroth law in the framework of the generalized thermodynamics is consistently recovered: as in the usual case, two systems which are in equilibrium with a third one are necessarily in equilibrium among them and share the same temperature.

Criticality of the discrete N-vector ferromagnet in a cubic lattice with a free surface

We study a discrete N-component spin ferromagnet with Hamiltonian βH= −NK∑〈i,j〉(Si·Sj)−N2L∑〈i,j〉(Si·Sj)2 in a semi-infinite cubic lattice. The coupling constants at the surface, Ks and Ls, are allowed to be different from the bulk ones, KB and LB. Using a simple real-space renormalization group procedure we obtain the N-evolution (N real) of the phase diagram, including the N→0 and N→∞ limits. The thermal (v) and crossover (φ) critical exponents at various critical and multicritical points are calculated.

Island coarsening in one-dimensional models with partially and completely reversible aggregation

Using computer simulations and scaling ideas, we study one-dimensional models of diffusion, aggregation and detachment of particles from islands in the post-deposition regime, i.e., without flux. The diffusion of isolated particles takes place with unit rate, aggregation occurs immediately upon contact with another particle or island, and detachment from an island occurs with rate e=exp(-E/kT), where E is the related energy barrier. In the partially reversible model, dissociation is limited to islands of size larger than a critical value i, while in the completely reversible model there is no restriction to that process (infinite i). Extending previous simulation results for the completely reversible case, we observe that a peaked island size distribution in the intermediate time regime, in which the mean island size is increasing, crosses over to the theoretically predicted exponentially decreasing distribution at long times. It contrasts with the partially reversible model, in which peaked distributions are obtained until the long time frozen state, which is attained with a crossover time τ∼i3/e. The mean island size at saturation varies as Ssat≈2i+Ce (C constant), while the completely reversible case shows an Arrhenius dependence of the mean island size, S∼e-1/2. Thus, for different coverages, the effect of the critical size i on the geometric features is much stronger than that of e, which may be used to infer the relevance of size-dependent detachment rates in real systems and other models.

Extraordinary transition for the anisotropic Heisenberg ferromagnet on a semi-infinite lattice

We obtain bulk and surface order parameters of the spin-12 anisotropic Heisenberg ferromagnet in a semi-infinite (d = 3) lattice, as functions of the temperature. This model is described by the Hamiltonian −β H = Σ〈i,j〉Kij[(1 − Δij)(σixσjx + σiyσiy) + σizσjz], where the coupling constant Kij and the anisotropy Δij equal KB and ΔB for bulk interactions and KS and ΔS for surface interactions. Using real-space renormalization-group techniques, we discuss the (possible) discontinuity on the first (or second) derivative of the surface magnetization at the extraordinary transition, where the surface maintains its magnetization as the bulk disorders. This transition has been extensively studied in the Ising case (Δ = 1), due to a controversy on the continuity of the first derivative of the surface magnetization at this point.

The anisotropic Heisenberg ferromagnet: Magnetization in a semi‐infinite lattice

Using a real space renormalization group procedure, we calculate both surface and bulk order parameters of the spin‐(1/2) anisotropic Heisenberg model in a semi‐infinite (d=3) lattice. We focus on the extraordinary transition, where the bulk disorders while the surface maintains its magnetization. We observe that the surface order parameter has a continuous first derivative at the bulk critical temperature, for all values of the anisotropy parameters ΔB and ΔS.

Magnetism of internal surfaces in a fractal structure

Abstract We study the inhomogeneous magnetization behavior of an Ising ferromagnet in Sierpinski pastry shells, using a real-space renormalization group approach. Two qualitatively different regions on the fractal are distinguished: the bulk and the set of internal surfaces which border the eliminated portions. We obtain the spontaneous mean magnetizations for these regions as a function of the temperature for different values of α = JS/JB (JS and JB are the internal surface and bulk coupling constants respectively) and different geometrical parameters b and l. The critical β exponents are obtained for the several transitions. We obtain different universality classes for the bulk transitions, depending on what occurs at the surfaces, and a step-like behavior of the magnetization as a function of the temperature of some values of b and l.