No Arabic abstract
We present Monte Carlo (MC) simulation studies of phase separation in binary (AB) mixtures with bond-disorder that is introduced in two different ways: (i) at randomly selected lattice sites and (ii) at regularly selected sites. The Ising model with spin exchange (Kawasaki) dynamics represents the segregation kinetics in conserved binary mixtures. We find that the dynamical scaling changes significantly by varying the number of disordered sites in the case where bond-disorder is introduced at the randomly selected sites. On the other hand, when we introduce the bond-disorder in a regular fashion, the system follows the dynamical scaling for the modest number of disordered sites. For higher number of disordered sites, the evolution morphology illustrates a lamellar pattern formation. Our MC results are consistent with the Lifshitz-Slyozov (LS) power-law growth in all the cases.
We have used the Monte Carlo (MC) simulation method with Metropolis algorithm to study the finite temperature phase transition properties of a binary alloy spherical nanoparticle with radius $r$ of the type $A_{p}B_{1-p}$. The system consists of two different species of magnetic components, namely, $A$ and $B$, and the components of the system have been selected $A$ and $B$ to be as $sigma = 1/2$ and $S=1$, respectively. A complete picture of phase diagrams, total magnetizations and susceptibilities in related planes have been presented, and the main roles of the radius of nanoparticle, active concentration value of type-$A$ atoms as well as other system parameters on the thermal and magnetic phase transition features of the considered system have been discussed in detail. Our MC investigations clearly show that it is possible to control the critical characteristic behaviors of the system with the help of adjustable Hamiltonian parameters.
A description of phase separation kinetics for solid binary (A,B) mixtures in thin film geometry based on the Kawasaki spin-exchange kinetic Ising model is presented in a discrete lattice molecular field formulation. It is shown that the model describes the interplay of wetting layer formation and lateral phase separation, which leads to a characteristic domain size $ell(t)$ in the directions parallel to the confining walls that grows according to the Lifshitz-Slyozov $t^{1/3}$ law with time $t$ after the quench. Near the critical point of the model, the description is shown to be equivalent to the standard treatments based on Ginzburg-Landau models. Unlike the latter, the present treatment is reliable also at temperatures far below criticality, where the correlation length in the bulk is only of the order of a lattice spacing, and steep concentration variations may occur near the walls, invalidating the gradient square approximation. A further merit is that the relation to the interaction parameters in the bulk and at the walls is always transparent, and the correct free energy at low temperatures is consistent with the time evolution by construction.
We perform Monte-Carlo simulations to study the Bernoulli ($p$) bond percolation on the enhanced binary tree which belongs to the class of nonamenable graphs with one end. Our numerical results show that the system has two different percolation thresholds $p_{c1}$ and $p_{c2}$. All the points in the intermediate phase $(p_{c1} < p < p_{c2})$ are critical and there exist infinitely many infinite clusters in the intermediate phase. In this phase the corresponding fractal exponent continuously increases with $p$ from zero to unity.
We analyze the critical properties of the three-dimensional Ising model with linear parallel extended defects. Such a form of disorder produces two distinct correlation lengths, a parallel correlation length $xi_parallel$ in the direction along defects, and a perpendicular correlation length $xi_perp$ in the direction perpendicular to the lines. Both $xi_parallel$ and $xi_perp$ diverge algebraically in the vicinity of the critical point, but the corresponding critical exponents $ u_parallel$ and $ u_perp$ take different values. This property is specific for anisotropic scaling and the ratio $ u_parallel/ u_perp$ defines the anisotropy exponent $theta$. Estimates of quantitative characteristics of the critical behaviour for such systems were only obtained up to now within the renormalization group approach. We report a study of the anisotropic scaling in this system via Monte Carlo simulation of the three-dimensional system with Ising spins and non-magnetic impurities arranged into randomly distributed parallel lines. Several independent estimates for the anisotropy exponent $theta$ of the system are obtained, as well as an estimate of the susceptibility exponent $gamma$. Our results corroborate the renormalization group predictions obtained earlier.
We review understanding of kinetics of fluid phase separation in various space dimensions. Morphological differences, percolating or disconnected, based on overall composition in a binary liquid or density in a vapor-liquid system, have been pointed out. Depending upon the morphology, various possible mechanisms and corresponding theoretical predictions for domain growth are discussed. On computational front, useful models and simulation methodologies have been presented. Theoretically predicted growth laws have been tested via molecular dynamics simulations of vapor-liquid transitions. In case of disconnected structure, the mechanism has been confirmed directly. This is a brief review on the topic for a special issue on coarsening dynamics, expected to appear in Comptes Rendus Physique.