Macroscopically constrained Wang-Landau method for systems with multiple order parameters and its application to drawing complex phase diagrams.

A generalized approach to Wang-Landau simulations, macroscopically constrained Wang-Landau, is proposed to simulate the density of states of a system with multiple macroscopic order parameters. The method breaks a multidimensional random-walk process in phase space into many separate, one-dimensional random-walk processes in well-defined subspaces. Each of these random walks is constrained to a different set of values of the macroscopic order parameters. When the multivariable density of states is obtained for one set of values of fieldlike model parameters, the density of states for any other values of these parameters can be obtained by a simple transformation of the total system energy. All thermodynamic quantities of the system can then be rapidly calculated at any point in the phase diagram. We demonstrate how to use the multivariable density of states to draw the phase diagram, as well as order-parameter probability distributions at specific phase points, for a model spin-crossover material: an antiferromagnetic Ising model with ferromagnetic long-range interactions. The fieldlike parameters in this model are an effective magnetic field and the strength of the long-range interaction.

Monte Carlo simulations of the critical properties of a Ziff-Gulari-Barshad model of catalytic CO oxidation with long-range reactivity.

The Ziff-Gulari-Barshad (ZGB) model, a simplified description of the oxidation of carbon monoxide (CO) on a catalyst surface, is widely used to study properties of nonequilibrium phase transitions. In particular, it exhibits a nonequilibrium, discontinuous transition between a reactive and a CO poisoned phase. If one allows a nonzero rate of CO desorption (k), the line of phase transitions terminates at a critical point (k(c)). In this work, instead of restricting the CO and atomic oxygen (O) to react to form carbon dioxide (CO(2)) only when they are adsorbed in close proximity, we consider a modified model that includes an adjustable probability for adsorbed CO and O atoms located far apart on the lattice to react. We employ large-scale Monte Carlo simulations for system sizes up to 240×240 lattice sites, using the crossing of fourth-order cumulants to study the critical properties of this system. We find that the nonequilibrium critical point changes from the two-dimensional Ising universality class to the mean-field universality class upon introducing even a weak long-range reactivity mechanism. This conclusion is supported by measurements of cumulant fixed-point values, cluster percolation probabilities, correlation-length finite-size scaling properties, and the critical exponent ratio ß/ν. The observed behavior is consistent with that of the equilibrium Ising ferromagnet with additional weak long-range interactions [T. Nakada, P. A. Rikvold, T. Mori, M. Nishino, and S. Miyashita, Phys. Rev. B 84, 054433 (2011)]. The large system sizes and the use of fourth-order cumulants also enable determination with improved accuracy of the critical point of the original ZGB model with CO desorption.

Model for the catalytic oxidation of CO, including gas-phase impurities and CO desorption.

We present results of kinetic Monte Carlo simulations of a modified Ziff-Gulari-Barshad model for the reaction CO+O → CO(2) on a catalytic surface. Our model includes impurities in the gas phase, CO desorption, and a modification known to eliminate the unphysical O poisoned phase. The impurities can adsorb and desorb on the surface, but otherwise remain inert. In a previous work that did not include CO desorption [Buendía and Rikvold, Phys. Rev. E 85, 031143 (2012)], we found that the impurities have very distinctive effects on the phase diagram and greatly diminish the reactivity of the system. If the impurities do not desorb, once the system reaches a stationary state, the CO(2) production disappears. When the impurities are allowed to desorb, there are regions where the CO(2) reaction window reappears, although greatly reduced. Following experimental evidence that indicates that temperature effects are crucial in many catalytic processes, here we further analyze these effects by including a CO desorption rate. We find that the CO desorption has the effect to smooth the transition between the reactive and the CO rich phase, and most importantly it can counteract the negative effects of the presence of impurities by widening the reactive window such that now the system remains catalytically active in the whole range of CO pressures.

Effects of inert species in the gas phase in a model for the catalytic oxidation of CO.

We study by kinetic Monte Carlo simulations the catalytic oxidation of carbon monoxide on a surface in the presence of contaminants in the gas phase. The process is simulated by a Ziff-Gulari-Barshad (ZGB) model that has been modified to include the effect of the contaminants and to eliminate an unphysical oxygen poisoned phase at very low CO partial pressures. The impurities can adsorb and desorb on the surface but otherwise remain inert. We find that if the impurities cannot desorb, no matter how small their proportion in the gas mixture, the reactive window and discontinuous transition to a CO poisoned phase at high CO pressures that characterize the original ZGB model disappear. The coverages become continuous, and once the surface has reached a steady state there is no production of CO(2). This is quite different from the behavior of systems in which the surface presents a fixed percentage of impurities. When the contaminants are allowed to desorb, the reactive phase appears again for CO pressures below a value that depends on the proportion of contaminants in the gas and on their desorption rate.

A new battery-charging method suggested by molecular dynamics simulations.

Based on large-scale molecular dynamics simulations, we propose a new charging method that should be capable of charging a lithium-ion battery in a fraction of the time needed when using traditional methods. This charging method uses an additional applied oscillatory electric field. Our simulation results show that this charging method offers a great reduction in the average intercalation time for Li(+) ions, which dominates the charging time. The oscillating field not only increases the diffusion rate of Li(+) ions in the electrolyte but, more importantly, also enhances intercalation by lowering the corresponding overall energy barrier.

Two modes of magnetization switching in a simulated iron nanopillar in an obliquely oriented field.

Finite-temperature micromagnetics simulations are employed to study the magnetization-switching dynamics driven by a field applied at an angle to the long axis of an iron nanopillar. A bimodal distribution in the switching times is observed, and evidence for two competing modes of magnetization-switching dynamics is presented. For the conditions studied here, temperature T = 20.2 K and the reversal field 3260 Oe at an angle of 75° to the long axis, approximately 60% of the switches involve unstable decay (no free-energy barrier) and 40% involve metastable decay (a free-energy barrier is crossed). The latter are indistinguishable from switches that are constrained to start at a metastable free-energy minimum. Competition between unstable and metastable decay may not be confined to the temperature studied in this paper, and could greatly complicate applications involving magnetization switching near the coercive field.

Effect of CO desorption and coadsorption with O on the phase diagram of a Ziff-Gulari-Barshad model for the catalytic oxidation of CO.

We study the effect of coadsorption of CO and O on a Ziff-Gulari-Barshad model with CO desorption for the reaction CO + O --> CO(2) on a catalytic surface. Coadsorption of CO at a surface site already occupied by an O is introduced by an Eley-Rideal-type mechanism that occurs with probability p, 0 < or = p < or = 1. We find that besides the well-known effect of eliminating the second-order phase transition between the reactive state and an O-poisoned state, the coadsorption step has a profound effect on the transition between the reactive state and the CO-poisoned state. The coexistence curve between these two states terminates at a critical value k(c) of the desorption rate k, which now depends on p. Our Monte Carlo simulations and finite-size scaling analysis indicate that k(c) decreases with increasing values of p. For p = 1, there appears to be a sharp phase transition between the two states only for k at (or near) zero.

Dynamic phase transition in the two-dimensional kinetic Ising model in an oscillating field: universality with respect to the stochastic dynamics.

We study the dynamical response of a two-dimensional Ising model subject to a square-wave oscillating external field. In contrast to earlier studies, the system evolves under a so-called soft Glauber dynamic [Rikvold and Kolesik, J. Phys. A 35, L117 (2002)], for which both nucleation and interface propagation are slower and the interfaces smoother than for the standard Glauber dynamic. We choose the temperature and magnitude of the external field such that the metastable decay of the system following field reversal occurs through nucleation and growth of many droplets of the stable phase, i.e., the multidroplet regime. Using kinetic Monte Carlo simulations, we find that the system undergoes a nonequilibrium phase transition, in which the symmetry-broken dynamic phase corresponds to an asymmetric stationary limit cycle for the time-dependent magnetization. The critical point is located where the half period of the external field is approximately equal to the metastable lifetime of the system. We employ finite-size scaling analysis to investigate the characteristics of this dynamical phase transition. The critical exponents and the fixed-point value of the fourth-order cumulant are found to be consistent with the universality class of the two-dimensional equilibrium Ising model. This universality class has previously been established for the same nonequilibrium model evolving under the standard Glauber dynamic, as well as in a different nonequilibrium model of CO oxidation. The results reported in the present paper support the hypothesis that this far-from-equilibrium phase transition is universal with respect to the choice of the stochastic dynamics.

Conjugate field and fluctuation-dissipation relation for the dynamic phase transition in the two-dimensional kinetic Ising model.

The two-dimensional kinetic Ising model, when exposed to an oscillating applied magnetic field, has been shown to exhibit a nonequilibrium, second-order dynamic phase transition (DPT), whose order parameter Q is the period-averaged magnetization. It has been established that this DPT falls in the same universality class as the equilibrium phase transition in the two-dimensional Ising model in zero applied field. Here we study the scaling of the dynamic order parameter with respect to a nonzero, period-averaged, magnetic "bias" field, H(b) for a DPT produced by a square-wave applied field. We find evidence that the scaling exponent, delta(d), of H(b) at the critical period of the DPT is equal to the exponent for the critical isotherm, delta(e), in the equilibrium Ising model. This implies that H(b) is a significant component of the field conjugate to Q. A finite-size scaling analysis of the dynamic order parameter above the critical period provides further support for this result. We also demonstrate numerically that, for a range of periods and values of H(b) in the critical region, a fluctuation-dissipation relation (FDR), with an effective temperature T(eff)(T,P,H0) depending on the period, and possibly the temperature and field amplitude, holds for the variables Q and H(b). This FDR justifies the use of the scaled variance of Q as a proxy for the nonequilibrium susceptibility, partial differential Q/partial differential H(b), in the critical region.

Suppressing roughness of virtual times in parallel discrete-event simulations.

In a parallel discrete-event simulation (PDES) scheme, tasks are distributed among processing elements (PEs) whose progress is controlled by a synchronization scheme. For lattice systems with short-range interactions, the progress of the conservative PDES scheme is governed by the Kardar-Parisi-Zhang equation from the theory of nonequilibrium surface growth. Although the simulated (virtual) times of the PEs progress at a nonzero rate, their standard deviation (spread) diverges with the number of PEs, hindering efficient data collection. We show that weak random interactions among the PEs can make this spread nondivergent. The PEs then progress at a nonzero, near-uniform rate without requiring global synchronizations.

Scaling analysis of polyacrylamide gel surfaces synthesized in the presence of surfactants.

Surfaces of polyacrylamide hydrogels synthesized in the presence of surfactants were imaged by atomic force microscopy (AFM), and the surface morphology was studied by numerical scaling analysis. The gels were formed by polymerizing acrylamide plus a cross-linker in the presence of surfactants, which were then removed by soaking in distilled water. Gels formed in the presence of over 20% surfactant (by weight) formed clear, but became opaque upon removal of the surfactants. Other gels formed and remained clear. The surface morphology of the gels was studied by several one- and two-dimensional numerical scaling methods. The surfaces were found to be self-affine on short length scales, with a roughness (Hurst) exponent in the range from 0.85 to 1, crossing over to a constant root-mean-square surface width at long scales. Both the crossover length between these two regimes and the saturation value of the surface width increased significantly with increasing surfactant concentration, coincident with the increase in opacity. We propose that the changes in the surface morphology are due to a percolation transition in the system of voids formed upon removal of the surfactants from the bulk.

Surface scaling analysis of a frustrated spring-network model for surfactant-templated hydrogels.

We propose and study a statistical-mechanical model, inspired by recent atomic force microscopy studies of the surface structures of crosslinked polymer gels into which voids are introduced through templating by surfactant micelles [M. Chakrapani et al., e-print cond-mat/0112255]. The gel is represented by a frustrated, triangular network of nodes connected by springs of random equilibrium lengths. The nodes represent crosslinkers, and the springs correspond to polymer chains. The boundaries are fixed at the bottom, free at the top, and periodic in the lateral direction. Voids are introduced by deleting a proportion of the nodes and their associated springs. The model is numerically relaxed to a representative local energy minimum, resulting in an inhomogeneous, "clumpy" bulk structure. The free top surface is defined at evenly spaced points in the lateral (x) direction by the height of the topmost spring, measured from the bottom layer, h(x). Its scaling properties are studied by calculating the root-mean-square surface width and the generalized increment correlation functions C(q)(x)=<|h(x(0)+x)-h(x(0))|(q)>. The surface is found to have a nontrivial scaling behavior on small length scales, with a crossover to scale-independent behavior on large scales. As the vacancy concentration approaches the site-percolation limit, both the crossover length and the saturation value of the surface width diverge in a manner that appears to be proportional to the bulk connectivity length. This suggests that a percolation transition in the bulk also drives a similar divergence observed in surfactant templated polyacrylamide gels at high surfactant concentrations.

Halide adsorption on single-crystal silver substrates: dynamic simulations and ab initio density functional theory.

We investigate the static and dynamic behaviors of a Br adlayer electrochemically deposited onto single-crystal Ag(100) using an off-lattice model of the adlayer. Unlike previous studies using a lattice-gas model, the off-lattice model allows adparticles to be located at any position within a two-dimensional approximation to the substrate. Interactions with the substrate are approximated by a corrugation potential. Using density functional theory (DFT) to calculate surface binding energies, a sinusoidal approximation to the corrugation potential is constructed. A variety of techniques, including Monte Carlo and Langevin simulations, are used to study the behavior of the adlayer. The lateral root-mean-square (rms) deviation of the adparticles from the binding sites is presented along with equilibrium coverage isotherms, and the thermally activated Arrhenius barrier-hopping model used in previous dynamic Monte Carlo simulations is tested.

Scaling analysis of a divergent prefactor in the metastable lifetime of a square-lattice Ising ferromagnet at low temperatures.

We examine a square-lattice nearest-neighbor Ising quantum ferromagnet coupled to d-dimensional phonon baths. Using the density-matrix equation, we calculate the transition rates between configurations, which determines the specific dynamic. Applying the calculated stochastic dynamic in Monte Carlo simulations, we measure the lifetimes of the metastable state. As the magnetic field approaches [H]/J=2 at low temperatures, the lifetime prefactor diverges because the transition rates between certain configurations approach zero under these conditions. Near [H]/J=2 and zero temperature, the divergent prefactor shows scaling behavior as a function of the field, temperature, and the dimension of the phonon baths. With proper scaling, the simulation data at different temperatures and for different dimensions of the baths collapse well onto two master curves, one for [H]/J>2 and one for [H]/J<2.

Absence of first-order transition and tricritical point in the dynamic phase diagram of a spatially extended bistable system in an oscillating field.

It has been well established that spatially extended, bistable systems that are driven by an oscillating field exhibit a nonequilibrium dynamic phase transition (DPT). The DPT occurs when the field frequency is of the order of the inverse of an intrinsic lifetime associated with the transitions between the two stable states in a static field of the same magnitude as the amplitude of the oscillating field. The DPT is continuous and belongs to the same universality class as the equilibrium phase transition of the Ising model in zero field [G. Korniss et al., Phys. Rev. E 63, 016120 (2001); H. Fujisaka et al., Phys. Rev. E 63, 036109 (2001)]. However, it has previously been claimed that the DPT becomes discontinuous at temperatures below a tricritical point [M. Acharyya, Phys. Rev. E 59, 218 (1999)]. This claim was based on observations in dynamic Monte Carlo simulations of a multipeaked probability density for the dynamic order parameter and negative values of the fourth-order cumulant ratio. Both phenomena can be characteristic of discontinuous phase transitions. Here we use classical nucleation theory for the decay of metastable phases, together with data from large-scale dynamic Monte Carlo simulations of a two-dimensional kinetic Ising ferromagnet, to show that these observations in this case are merely finite-size effects. For sufficiently small systems and low temperatures, the continuous DPT is replaced, not by a discontinuous phase transition, but by a crossover to stochastic resonance. In the infinite-system limit, the stochastic-resonance regime vanishes, and the continuous DPT should persist for all nonzero temperatures.

Dynamic phase transition in a time-dependent Ginzburg-Landau model in an oscillating field.

The Ginzburg-Landau model below its critical temperature in a temporally oscillating external field is studied both theoretically and numerically. As the frequency or the amplitude of the external field is changed, a nonequilibrium phase transition is observed. This transition separates spatially uniform, symmetry-restoring oscillations from symmetry-breaking oscillations. Near the transition a perturbation theory is developed, and a switching phenomenon is found in the symmetry-broken phase. Our results confirm the equivalence of the present transition to that found in Monte Carlo simulations of kinetic Ising systems in oscillating fields, demonstrating that the nonequilibrium phase transition in both cases belongs to the universality class of the equilibrium Ising model in zero field. This conclusion is in agreement with symmetry arguments [G. Grinstein, C. Jayaprakash, and Y. He, Phys. Rev. Lett. 55, 2527 (1985)] and recent numerical results [G. Korniss, C. J. White, P. A. Rikvold, and M. A. Novotny, Phys. Rev. E 63, 016120 (2001)]. Furthermore, a theoretical result for the structure function of the local magnetization with thermal noise, based on the Ornstein-Zernike approximation, agrees well with numerical results in one dimension.

Dynamic phase transition, universality, and finite-size scaling in the two-dimensional kinetic Ising model in an oscillating field.

We study the two-dimensional kinetic Ising model below its equilibrium critical temperature, subject to a square-wave oscillating external field. We focus on the multidroplet regime, where the metastable phase decays through nucleation and growth of many droplets of the stable phase. At a critical frequency, the system undergoes a genuine nonequilibrium phase transition, in which the symmetry-broken phase corresponds to an asymmetric stationary limit cycle for the time-dependent magnetization. We investigate the universal aspects of this dynamic phase transition at various temperatures and field amplitudes via large-scale Monte Carlo simulations, employing finite-size scaling techniques adopted from equilibrium critical phenomena. The critical exponents, the fixed-point value of the fourth-order cumulant, and the critical order-parameter distribution all are consistent with the universality class of the two-dimensional equilibrium Ising model. We also study the cross-over from the multidroplet regime to the strong-field regime, where the transition disappears.

Evolution of speckle during spinodal decomposition.

Time-dependent properties of the speckled intensity patterns created by scattering coherent radiation from materials undergoing spinodal decomposition are investigated by numerical integration of the Cahn-Hilliard-Cook equation. For binary systems which obey a local conservation law, the characteristic domain size is known to grow in time tau as R=[Btau](n) with n=1/3, where B is a constant. The intensities of individual speckles are found to be nonstationary, persistent time series. The two-time intensity covariance at wave vector k can be collapsed onto a scaling function Cov(deltat,t), where deltat=k(1/n)B(tau(2)-tau(1)) and t=k(1/n)B(tau(1)+tau(2))/2. Both analytically and numerically, the covariance is found to depend on deltat only through deltat/t in the small-t limit and deltat/t (1-n) in the large-t limit, consistent with a simple theory of moving interfaces that applies to any universality class described by a scalar order parameter. The speckle-intensity covariance is numerically demonstrated to be equal to the square of the two-time structure factor of the scattering material, for which an analytic scaling function is obtained for large t. In addition, the two-time, two-point order-parameter correlation function is found to scale as C(r/(B(n)sqaureroot[tau1(2n)+tau2(2n)]),tau1/tau2), even for quite large distances r. The asymptotic power-law exponent for the autocorrelation function is found to be lambda approximately 4.47, violating an upper bound conjectured by Fisher and Huse.