Finite-size scaling studies of one-dimensional reaction-diffusion systems. Part II. Numerical methods

The scaling exponent and the scaling function for the 1D single-species coagulation model (A+AA) are shown to be universal, i.e., they are not influenced by the value of the coagulation rate. They are independent of the initial conditions as well. Two different numerical methods are used to compute the scaling properties of the concentration: Monte Carlo simulations and extrapolations of exact finite-lattice data. These methods are tested in a case where analytical results are available. To obtain reliable results from finite-size extrapolations, numerical data for lattices up to ten sites are sufficient.     

Nonsymmetric first-order transitions: Finite-size scaling and tests for infinite-range models

Finite-size rounding of first-order transitions is studied for the general case of nonsymmetric phases and nonperiodic boundary conditions. The main features include the surface-induced shift of the rounded transition on the scale 1/L, while the order parameter discontinuity is rounded on the scale 1/L ^d. This rounding is described by the universal scaling forms with scaling functions identical to those for the periodic, symmetric case. The proposed formalism applies to scalar-order-parameter, single-domain systems. It is tested by exact calculations for a class of infinite-range models.     

Monte Carlo study of the generalized reaction-diffusion lattice-gas model system

The reaction-diffusion lattice-gas model is an interacting particle system out of equilibrium whose microscopic dynamics is a combination of Glauber (reaction) and Kawasaki (diffusion) processes; the Glauber ratec(s; x) at sitex when the configuration iss satisfies detailed balance at temperatureT, while the Kawasaki ratec(s; x, y) between nearest-neighbor sitesx andy satisfies detailed balance at a different temperatureT. We report on the phase diagram of that system as obtained from a series of Monte Carlo simulations of steady states in two-dimensional lattices with arbitrary values forT,T, and; this generalizes previous analytical and numerical studies for and/orT. When the rates are implemented by the Metropolis algorithm, the system is observed to undergo various types of first- and second-order (nonequilibrium) phase transitions, e.g., one may identify Onsager (equilibrium) as well as Landau (mean-field) types of continuous phase transitions.Dedicated to Joel L. Lebowitz on the occasion of his 60th birthday.     

Optimized analysis of the critical behavior in polymer mixtures from Monte Carlo simulations

A complete outline is given for how to determine the critical properties of polymer mixtures with extrapolation methods similar to the Ferrenberg-Swendsen techniques recently devised for spin systems. By measuring not only averages but the whole distribution of the quantities of interest, it is possible to extrapolate the data obtained in only a few simulations nearT _c over the entire critical region, thereby saving at least 90% of the computer time normally needed to locate susceptibility peaks or cumulant intersections and still getting more precise results. A complete picture of the critical properties of polymer mixtures in the thermodynamic limit is then obtained with finite-size scaling functions. Since the amount of information extracted from a simulation in this way is drastically increased as compared to conventional methods, the investigation of mixtures with long chains or built-in asymmetries is now possible. As an example, the critical points, exponents, and amplitudes of dense, symmetric polymer mixtures with chain lengths ranging fromN=16 up toN=256 are determined within the framework of the 3D bond fluctuation model using grand canonical simulation techniques. As an example for an asymmetry, the generalization of the method to asymmetric monomer potentials is briefly discussed.     

Non-universal critical behaviour of heteronuclear dimers on a square lattice––A Monte Carlo study

Monte Carlo simulation within the grand canonical ensemble, the histogram reweighting technique, and finite size scaling analysis are used to explore the phase behaviour of heteronuclear dimers, composed of A and B type atoms, on a square lattice. We have found that for the models with attractive BB and AB nearest-neighbour energy, u_BB=u_AB=−1, and for non-repulsive energy between AA nearest-neighbour sites, u_AA<0, the system belongs to the universality class of the two-dimensional Ising model. However, when u_AA>0, the system exhibits a non-universal critical behaviour. We have evaluated the dependences of the critical point characteristics on the value of u_AA.     

Overcoming artificial spatial correlations in simulations of superstructure domain growth with parallel Monte Carlo algorithms

We study the applicability of parallelized/vectorized Monte Carlo (MC) algorithms to the simulation of domain growth in two-dimensional lattice gas models undergoing an ordering process after a rapid quench below an order-disorder transition temperature. As examples we consider models with 2×1 andc(2×2) equilibrium superstructures on the square and rectangular lattices, respectively. We also study the case of phase separation (1×1 islands) on the square lattice. A generalized parallel checkerboard algorithm for Kawasaki dynamics is shown to give rise to artificial spatial correlations in all three models. However, only ifsuperstructure domains evolve do these correlations modify the kinetics by influencing the nucleation process and result in a reduced growth exponent compared to the value from the conventional heat bath algorithm with random single-site updates. In order to overcome these artificial modifications, two MC algorithms with a reduced degree of parallelism (hybrid and mask algorithms, respectively) are presented and applied. As the results indicate, these algorithms are suitable for the simulation of superstructure domain growth on parallel/vector computers.     

Monte Carlo study on bilayer thin films magnetic properties dependence with discontinouos anisotropy parameters

In the last few years there has been significant interest in the field of thin films, due to numerous specific phenomena related to the low dimension of these systems, and to the large opportunities in development of high technologies based on their specific magnetic and electronic properties. When dealing with systems of reduced dimensionality it is important to take into account the influence of magnetic anisotropies. In this paper we investigate the magnetic properties of bilayer thin film. This behavior is modeled using Monte Carlo simulations, in the Extended Anisotropic Heisenberg Model. The magnetization, out-of-plane and in-plane magnetic susceptibilities, and also the specific heat bearings according to temperature are investigated in order to find the potential magnetic ordering phases and the critical temperatures, for two sets parameter assignments. For quasi-uniform anisotropy parameters of the film we detect the ferromagnetism-paramagnetism transition and then, by changing the model parameters values, we relieve a short range ferromagnetic ordering phase arising from the antiferromagnetic base layer coupling influence and from easy-plane anisotropy discontinuity on the layers interface.      

Phase equilibrium of Cd_(1-x)Zn_xS alloys studied by first-principles calculations and Monte Carlo simulations

The first-principles calculations based on density functional theory combined with cluster expansion techniques and Monte Carlo(MC) simulations were used to study the phase diagrams of both wurtzite(WZ) and zinc-blende(ZB)Cd_(1-x)Zn_xS alloys.All formation energies are positive for WZ and ZB Cd_(1-x)Zn_xS alloys,which means that the Cd_(1-x)Zn_xS alloys are unstable and have a tendency to phase separation.For WZ and ZB Cd_(1-x)Zn_xS alloys,the consolute temperatures are 655 K and 604 K,respectively,and they both have an asymmetric miscibility gap.We obtained the spatial distributions of Cd and Zn atoms in WZ and ZB Cd_(0.5)Zn_(0.5)S alloys at different temperatures by MC simulations.We found that both WZ and ZB phases of Cd_(0.5)Zn_(0.5)S alloy exhibit phase segregation of Cd and Zn atoms at low temperature,which is consistent with the phase diagrams.     

Monte Carlo simulation of the compensation and critical behaviors of a ferrimagnetic core/shell nanoparticle Ising model

A Monte Carlo simulation has been used to study the magnetic properties and the critical behaviors of a single spherical nanoparticle, consisting of a ferromagnetic core of spins surrounded by a ferromagnetic shell of S=±1, 0 or , spins with antiferromagnetic interface coupling, located on a simple cubic lattice. A number of characteristic phenomena has been found. In particular, the effects of the shell coupling and the interface coupling on both the critical and compensation temperatures are investigated. We have found that, for appropriate values of the system parameters, two compensation temperatures may occur in the present system.     

Dynamic percolation transition induced by phase separation: A Monte Carlo analysis

The percolation transition of geometric clusters in the three-dimensional, simple cubic, nearest neighbor Ising lattice gas model is investigated in the temperature and concentration region inside the coexistence curve. We consider quenching experiments, where the system starts from an initially completely random configuration (corresponding to equilibrium at infinite temperature), letting the system evolve at the considered temperature according to the Kawasaki spinexchange dynamics. Analyzing the distributionn _l(t) of clusters of sizel at timet, we find that after a time of the order of about 100 Monte Carlo steps per site a percolation transition occurs at a concentration distinctly lower than the percolation concentration of the initial random state. This dynamic percolation transition is analyzed with finite-size scaling methods. While at zero temperature, where the system settles down at a frozen-in cluster distribution and further phase separation stops, the critical exponents associated with this percolation transition are consistent with the universality class of random percolation, the critical behavior of the transient time-dependent percolation occurring at nonzero temperature possibly belongs to a different, new universality class.     

Random-bond Ising chain in a transverse magnetic field: A finite-size scaling analysis

We investigate the zero-temperature quantum phase transition of the randombond Ising chain in a transverse magnetic field. Its critical properties are identical to those of the McCoy-Wu model, which is a classical Ising model in two dimensions with layered disorder. The latter is studied via Monte Carlo simulations and transfer matrix calculations and the critical exponents are determined with a finite-size scaling analysis. The magnetization and susceptibility obey conventional rather than activated scaling. We observe that the order parameter and correlation function probability distribution show a nontrivial scaling near the critical point, which implies a hierarchy of critical exponents associated with the critical behavior of the generalized correlation lengths.     

Surface effects on liquid crystals constrained in nanoscaled pores investigated by field cycling NMR relaxometry and Monte Carlo simulations

Proton relaxation rates of nematic liquid crystals confined in nanoporous cavities were measured in a broad frequency range with the help of field cycling nuclear magnetic resonance relaxometry. The shape of relaxation dispersion curves in confined materials strongly deviates from the behavior in bulk, both above and below the bulk isotropization temperature. A strong increase in relaxation rates, exceeding by two orders of magnitude that of the bulk sample, is observed in the range of a few kilohertz. Relaxation rates in bigger pores decreased. Experimental findings are interpreted in terms of surface-induced orientational order and diffusion between sites with different orientations of local directors. With the aid of Monte Carlo simulations, two processes affecting low-frequency relaxation could be identified: (a) exchange losses of molecules from the surface-ordered phase to the bulk-like phase, and (b) Reorientations Mediated by Translational Displacements, which dominate the long-time scale and account for the recovery of correlation in molecular orientations as molecules probe different surface sites. It is shown that the width of the oriented layer may strongly affect the slope of dispersion curves and that cross-over between plateau and power law dispersion regimes shifts towards lower frequencies for bigger pores.     

TLD measurements and Monte Carlo simulations for glandular dose and scatter fraction assessment in mammography: A comparative study

The main purpose of this study was to validate and compare Mean Glandular Dose (MGD) values obtained using Monte Carlo simulations with experimental values obtained from Entrance Surface Dose (ESD) and depth dose measurements performed in a Hospital mammography unit. ESD and depth dose were measured using ThermoLuminescent Dosimeters (TLDs), and a tissue equivalent mammography phantom recommended by the American College of Radiology (ACR). Measurements and Monte Carlo simulations were also compared with the MGD calculated using the Automatic Exposure Control (AEC) system of the mammographic unit. In the simulations the Doppler energy broadening effect was also taken into account. The simulated ESD are about 5%–10% higher than the measured ESD values. The deviation between the measured and simulated MGD values in the phantom is of about 15%. The MGD evaluated using the AEC system is smaller both with respect to the Monte Carlo simulation and experimental result by a factor of about 15% and 25% respectively. Moreover the BackScatter Factor (BSF) estimated by Monte Carlo simulations was used for the MGD calculation according to the Wu’s method. Finally the inclusion of the energy broadening effect on MGD calculation produces negligible variations on the simulated results.     

Monte Carlo study of the critical behavior of pure and site-diluted Ising ferro-and ferrimagnets

Monte Carlo simulations are performed for pure and site-diluted Ising ferro- and ferrimagnets on a simple cubic lattice with up to 40³ sites and with impurity concentrationx. For the diluted ferromagnet (x=0.2) the exponent= 0.392±0.03 is definitely larger than the pure model value of=0.304±0.03. In contrast, for ferrimagnetic systems (x=0, 0.1, 0.2) the values appear to be independent ofx and within the error limits consistent with the value for the pure ferromagnet, possibly because the width of the asymptotic random critical regime (or of the crossover regime) is even smaller than in the case of ferromagnets.     

Adsorption in one-dimensional channels arranged in a triangular structure: Theory and Monte Carlo simulations

Adsorption thermodynamics of interacting particles adsorbed on one-dimensional channels arranged in a triangular cross-sectional structure is studied through Bragg-Williams approximation (BWA), Monte Carlo (MC) simulations and the recently reported Effective Substates approximation (ESA) [J.L. Riccardo, G. Zgrablich, W. A. Steele, Appl. Surf. Sci. 196 (2002) 138]. Two kinds of lateral interaction energies have been considered: (1) w_L, interaction energy between nearest-neighbor particles adsorbed along a single channel and (2) w_T, interaction energy between particles adsorbed across nearest-neighbor channels. We focus on the case of repulsive transversal interactions (w_T>0), for which a rich variety of ordered phases are observed in the adlayer, depending on the value of the parameters k_BT/w_T (being k_B the Boltzmann constant) and w_L/w_T. Comparisons between analytical data and MC simulations are performed in order to test the validity of the theoretical models. Appreciable differences can be seen for the different approximations, ESA being the most accurate for all cases.     

Finite-size effects and phase transition in the three-dimensional three-state Potts model

The three-state Potts model in three dimensions is studied by Monte Carlo and finite-size scaling techniques. Using a histogram method recently proposed by Ferrenberg and Swendsen, the finite-size dependence for the maximum of the specific heat is found to scale with the volume of the system, indicating that the phase transition is of first order. The value of the latent heat per spin and the correlation length at the transition are estimated.     

Multicanonical Monte Carlo simulations on intramolecular micelle formation in copolymers

The formation of intramolecular micelles in copolymers with periodic sequence, where hydrophobic units (stickers) are periodically placed along the chain, is studied by using multicanonical Monte Carlo computer simulations for an off-lattice bead-rod model in three dimensions. With decreasing the temperature, a transition from random-coil conformations to micelles occurs and flower-type micelles are formed via the transition. The number of stickers forming a micelle core is limited by the excluded-volume effect of loop chains around micelle cores. By this effect, two intramolecular micelles are formed for long polymer chains with 60 bonds via the coil-to-micelle transition. By further decreasing the temperature, we find that another transition, i.e., a micelle-to-micelle transition, takes place. At this transition point, the two intramolecular micelles merge into one micelle. Furthermore, we extend the multicanonical MC method to study elastic properties of single polymer chains with strong attractive interactions under external force fields, and study how the intramolecular micellization affects the elastic property of single polymer chains.