Domain Wall Migration in 3-d in the Presence of Diffusing Impurities

A new three-dimensional simulation procedure was developed for domain wall (grain boundary, APB, magnetic, etc.) migration in the presence of diffusing impurities. The simulation is based upon a kinetic Monte Carlo algorithm and an extended Ising model, incorporating both conserved and non-conserved dynamics. The simulations show a dependence of the domain wall velocity on driving force which is very similar to that seen in 2-d and in qualitative agreement with experiment. That is, the presence of a low mobility regime at small driving force and an abrupt transition to a high mobility regime at larger forces, under some conditions, and a continuous, non-linear dependence of the velocity on the force in others. The main qualitative difference between the 2-d and 3-d simulation results is in how the domain wall roughness depends on driving force. The velocity-driving force relation is not consistent with classic continuum models, but may be described, in the high velocity regime, by a theory based upon a discrete version of these models.     

An On-Line Library of Extended High-Temperature Expansions of Basic Observables for the Spin-S Ising Models on Two- and Three-Dimensional Lattices

We present an on-line library of unprecedented extension for high-temperature expansions of basic observables in the Ising models of general spin S, with nearest-neighbor interactions. We have tabulated through order ²⁵ the series for the nearest-neighbor correlation function, the susceptibility and the second correlation moment in two dimensions on the square lattice, and, in three dimensions, on the simple-cubic and the body-centered cubic lattices. The expansion of the second field derivative of the susceptibility is also tabulated through ²³ for the same lattices. We have thus added several terms (from four up to thirteen) to the series already published for spin S = 1/2, 1, 3/2, 2, 5/2, 3, 7/2, 4, 5, .     

Decay of the remanent magnetization in the asymmetric spin chain

The dynamics of the one-dimensional spin glass with asymmetric interactions between neighboring spins is considered. We confine ourselves to discrete couplings with values ±J. We show that the algebraic decay of the remanent magnetization of the infinite ±J-spin chain at zero temperature is only valid for symmetric couplings. Our analytical investigations as well as computer simulations show stretched exponential decay for any finite concentration of antisymmetric bonds. Thus, the asymmetric ±J-spin chain shows an asymmetry-induced phase transition at zero temperature.     

Theory of interfacial phase transitions in surfactant systems

The spin-1 Ising model, which is equivalent to the three-component lattice gas model, is used to study wetting transitions in three-component surfactant systems consisting of an oil, water, and a nonionic surfactant. Phase equilibria, interfacial profiles, and interfacial tensions for three-phase equilibrium are determined in mean field approximation, for a wide range of temperature and interaction parameters. Surfactant interaction parameters are found to strongly influence interfacial tensions, reducing them in some cases to ultralow values. Interfacial tensions are used to determine whether the middle phase, rich in surfactant, wets or does not wet the interface between the oil-rich and water-rich phases. By varying temperature and interaction parameters, a wetting transition is located and found to be of the first order. Comparison is made with recent experimental results on wetting transitions in ternary surfactant systems.This paper is dedicated to J. K. Percus in honor of his 65th birthday.     

Interface motion in a two-dimensional Ising model with a field

We determine by Monte Carlo simulations the width of an interface between the stable phase and the metastable phase in a two-dimensional Ising model with a magnetic field, in the case of nonconversed order parameter (Glauber dynamics). At zero temperature, the width increases ast with–1/3, as predicted by earlier theories. As temperature increases, the value of the effective exponent that we measure decreases toward the value 1/4, which is the value in the absence of magnetic field.     

Effect of disorder on relaxation in the one-dimensional Glauber model

We study the long-time relaxation of magnetization in a disordered linear chain of Ising spins from an initially aligned state. The coupling constants are ferromagnetic and nearest-neighbor only, taking valuesJ ₀ andJ ₁ with probabilitiesp and 1–p, respectively. The time evolution of the system is governed by the Glauber master equation. It is shown that for large timest, the magnetizationM(t) varies as [exp(–₀ t](t), where ₀ is a function of the stronger bond strengthJ ₀ only, and (t) decreases slower than an exponential. For very long times, we find that ln (t) varies as –t ^1/3. For low enough temperatures, there is an intermediate time regime when ln (t) varies as –t ^1/2. The results can be extended to more general probability distributions of ferromagnetic coupling constants, assuming thatM(t) can only increase if any bond in the chain is strengthened. If the coupling constants have a continuous distribution in which the probability density varies as a power law near some maximum valueJ ₀, we find that ln (t) varies as –t ^1/3(lnt)^2/3 for large times.     

Seeded Ising Model and Distributed Biometric Template Storage and Matching

It is known that a variant of Ising model, called Seeded Ising Model, can be used to recover the information content of a biometric template from a fraction of information therein. The method consists in reconstructing the whole template, which is called the intruder template in this paper, using only a small portion of the given template, a partial template. This reconstruction method may pose a security threat to the integrity of a biometric identity management system. In this paper, based on the Seeded Ising Model, we present a systematic analysis of the possible security breach and its probability of accepting the intruder templates as genuine. Detailed statistical experiments on the intruder match rate are also conducted under various scenarios. In particular, we study (1) how best a template is divided into several small pieces called partial templates, each of which is to be stored in a separate silo; (2) how to do the matching by comparing partial templates in the locked-up silos, and letting only the results of these intra-silo comparisons be sent to the central tallying server for final scoring without requiring the whole templates in one location at any time.     

Analytical Expressions for Ising Models on High Dimensional Lattices

We use an m-vicinity method to examine Ising models on hypercube lattices of high dimensions d≥3. This method is applicable for both short-range and long-range interactions. We introduce a small parameter, which determines whether the method can be used when calculating the free energy. When we account for interaction with the nearest neighbors only, the value of this parameter depends on the dimension of the lattice d. We obtain an expression for the critical temperature in terms of the interaction constants that is in a good agreement with the results of computer simulations. For d=5,6,7, our theoretical estimates match the numerical results both qualitatively and quantitatively. For d=3,4, our method is sufficiently accurate for the calculation of the critical temperatures; however, it predicts a finite jump of the heat capacity at the critical point. In the case of the three-dimensional lattice (d=3), this contradicts the commonly accepted ideas of the type of the singularity at the critical point. For the four-dimensional lattice (d=4), the character of the singularity is under current discussion. For the dimensions d=1, 2 the m-vicinity method is not applicable.     

Electrostatic potential in cylindrical dielectric media using the image charge method

We derive a simple analytical expression for the electric potential produced by a point charge in a cylindrical pore with relative permittivity different from that of the surrounding medium. The interface between the pore and the surrounding media may contain electric charge or be electrically neutral. The expression reduces to the known solutions when the surrounding dielectric medium is identical to the pore or an electric conductor. We discuss the convergence of the series expansion and numerically evaluate the electrostatic potential inside the cylindrical pore. The calculated potential shows the effect of the dielectric permittivity difference of the media. The results demonstrate that the expression can be implemented in a numerical dynamic simulation of charged systems in cylindrical geometry. We also give an expression for the case when the source charge is in the medium outside the cylinder.