arXiv subjects

P. A. Rikvold

Publications and source records attributed to P. A. Rikvold.

At least 73 records · Page 4Linked to original sources

arXiv2000

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 multi-droplet 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 non-equilibrium 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 multi-droplet to the strong-field regime, where the transition disappears.

cond-mat.stat-mech↗

arXiv2000

Dynamics of Br Electrosorption on Single-Crystal Ag(100): A Computational Study

We present dynamic Monte Carlo simulations of a lattice-gas model for bromine electrodeposition on single-crystal silver (100). This system undergoes a continuous phase transition between a disordered phase at low electrode potentials and a commensurate c(2X2) phase at high potentials. The lattice-gas parameters are determined by fitting simulated equilibrium adsorption isotherms to chronocoulometric data, and free-energy barriers for adsorption/desorption and lateral diffusion are estimated from ab initio data in the literature. Cyclic voltammograms in the quasi-static limit are obtained by equilibrium Monte Carlo simulations, while for nonzero potential scan rates we use dynamic Monte Carlo simulation. The butterfly shapes of the simulated voltammograms are in good agreement with experiments. Simulated potential-step experiments give results for the time evolution of the Br coverage, as well as the c(2X2) order parameter and its correlation length. During phase ordering following a positive potential step, the system obeys dynamic scaling. The disordering following a negative potential step is well described by random desorption with diffusion. Both ordering and disordering processes are strongly influenced by the ratio of the time scales for desorption and diffusion. Our results should be testable by experiments, in particular cyclic voltammetry and surface X-ray scattering.

cond-mat.mtrl-sci↗

arXiv2000

Fine-grid Simulations of Thermally Activated Switching in Nanoscale Magets

Numerical integration of the Landau-Lifshitz-Gilbert equation with thermal fluctuations is used to study the dynamic response of single-domain nanomagnets to rapid changes in the applied magnetic field. The simulation can resolve magnetization patterns within nanomagnets and uses the Fast Multipole method to calculate dipole-dipole interactions efficiently. The thermal fluctuations play an essential part in the reversal process whenever the applied field is less than the zero-temperature coercive field. In this situation pillar-shaped nanomagnets are found to reverse through a local curling mode that involves the formation and propagation of a domain wall. Tapering the ends of the pillars to reduce pole-avoidance effects changes the energies involved but not the fundamental process. The statistical distribution of switching times is well described by the independent nucleation and subsequent growth of regions of reversed magnetization at both ends of the pillar.

cond-mat.mtrl-sci↗

arXiv2000

Hysteresis in an Electrochemical System: Br Electrodeposition on Ag(100)

We examine hysteresis in cyclic voltammetry of Br electrosorption onto single-crystal Ag(100) by dynamic Monte Carlo simulations. At room temperature, this system displays a second-order phase transition from a low-coverage disordered phase to a doubly degenerate $c (2 \times 2)$ phase. The electrochemical potential is ramped back and forth across the phase transition, linearly in time, and the phase lag between the response of the adlayer and the potential is observed to depend on the sweep rate. The hysteresis in this system is caused by slow ordering/disordering kinetics and critical slowing-down.

cond-mat.mtrl-sci↗

arXiv2000

Non-equilibrium Surface Growth and Scalability of Parallel Algorithms for Large Asynchronous Systems

The scalability of massively parallel algorithms is a fundamental question in computer science. We study the scalability and the efficiency of a conservative massively parallel algorithm for discrete-event simulations where the discrete events are Poisson arrivals. The parallel algorithm is applicable to a wide range of problems, including dynamic Monte Carlo simulations for large asynchronous systems with short-range interactions. The evolution of the simulated time horizon is analogous to a growing and fluctuating surface, and the efficiency of the algorithm corresponds to the density of local minima of this surface. In one dimension we find that the steady state of the macroscopic landscape is governed by the Edwards-Wilkinson Hamiltonian, which implies that the algorithm is scalable. Preliminary results for higher-dimensional logical topologies are discussed.

cond-mat.stat-mech↗

arXiv2000

From Massively Parallel Algorithms and Fluctuating Time Horizons to Non-equilibrium Surface Growth

We study the asymptotic scaling properties of a massively parallel algorithm for discrete-event simulations where the discrete events are Poisson arrivals. The evolution of the simulated time horizon is analogous to a non-equilibrium surface. Monte Carlo simulations and a coarse-grained approximation indicate that the macroscopic landscape in the steady state is governed by the Edwards-Wilkinson Hamiltonian. Since the efficiency of the algorithm corresponds to the density of local minima in the associated surface, our results imply that the algorithm is asymptotically scalable.

cond-mat.stat-mech↗

arXiv1999

Simulations of metastable decay in two- and three-dimensional models with microscopic dynamics

We present a brief analysis of the crossover phase diagram for the decay of a metastable phase in a simple dynamic lattice-gas model of a two-phase system. We illustrate the nucleation-theoretical analysis with dynamic Monte Carlo simulations of a kinetic Ising lattice gas on square and cubic lattices. We predict several regimes in which the metastable lifetime has different functional forms, and provide estimates for the crossovers between the different regimes. In the multidroplet regime, the Kolmogorov-Johnson-Mehl-Avrami theory for the time dependence of the order-parameter decay and the two-point density correlation function allows extraction of both the order parameter in the metastable phase and the interfacial velocity from the simulation data.

cond-mat.mtrl-sci↗

arXiv1999

Dynamic Phase Transition and Hysteresis in Kinetic Ising Models

We briefly introduce hysteresis in spatially extended systems and the dynamic phase transition observed as the frequency of the oscillating field increases beyond a critical value. Hysteresis and the decay of metastable phases are closely related phenomena, and a dynamic phase transition can occur only for field amplitudes, temperatures, and system sizes at which the metastable phase decays through nucleation and growth of many droplets. We present preliminary results from extensive Monte Carlo simulations of a two-dimensional kinetic Ising model in a square-wave oscillating field and estimate critical exponents by finite-size scaling techniques adapted from equilibrium critical phenomena. The estimates are consistent with the universality class of the two-dimensional equilibrium Ising model and inconsistent with two-dimensional random percolation. However, we are not aware of any theoretical arguments indicating why this should be so. Thus, the question of the universality class of this nonequilibrium critical phenomenon remains open.

cond-mat.stat-mech↗

arXiv1998

Parallelization of a Dynamic Monte Carlo Algorithm: a Partially Rejection-Free Conservative Approach

We experiment with a massively parallel implementation of an algorithm for simulating the dynamics of metastable decay in kinetic Ising models. The parallel scheme is directly applicable to a wide range of stochastic cellular automata where the discrete events (updates) are Poisson arrivals. For high performance, we utilize a continuous-time, asynchronous parallel version of the n-fold way rejection-free algorithm. Each processing element carries an lxl block of spins, and we employ the fast SHMEM-library routines on the Cray T3E distributed-memory parallel architecture. Different processing elements have different local simulated times. To ensure causality, the algorithm handles the asynchrony in a conservative fashion. Despite relatively low utilization and an intricate relationship between the average time increment and the size of the spin blocks, we find that for sufficiently large l the algorithm outperforms its corresponding parallel Metropolis (non-rejection-free) counterpart. As an example application, we present results for metastable decay in a model ferromagnetic or ferroelectric film, observed with a probe of area smaller than the total system.

cond-mat.stat-mech↗

arXiv1998

Kinetic Ising model in an oscillating field: Avrami theory for the hysteretic response and finite-size scaling for the dynamic phase transition

Hysteresis is studied for a two-dimensional, spin-1/2, nearest-neighbor, kinetic Ising ferromagnet in an oscillating field, using Monte Carlo simulations and analytical theory. Attention is focused on large systems and strong field amplitudes at a temperature below T_c. In this parameter regime, the magnetization switches through random nucleation and subsequent growth of many droplets of spins aligned with the applied field. Using a time-dependent extension of the Kolmogorov-Johnson-Mehl-Avrami (KJMA) theory of metastable decay, we analyze the statistical properties of the hysteresis-loop area and the correlation between the magnetization and the applied field. This analysis enables us to accurately predict the results of extensive Monte Carlo simulations. The average loop area exhibits an extremely slow approach to an asymptotic, logarithmic dependence on the product of the amplitude and the frequency of the applied field. This may explain the inconsistent exponent estimates reported in previous attempts to fit experimental and numerical data for the low-frequency behavior of this quantity to a power law. At higher frequencies we observe a dynamic phase transition. Applying standard finite-size scaling techniques from the theory of second-order equilibrium phase transitions to this nonequilibrium phase transition, we obtain estimates for the transition frequency and the critical exponents (beta/nu \approx 0.11, gamma/nu \approx 1.84 and nu \approx 1.1). In addition to their significance for the interpretation of recent experiments on switching in ferromagnetic and ferroelectric nanoparticles and thin films, our results provide evidence for the relevance of universality and finite-size scaling to dynamic phase transitions in spatially extended nonstationary systems.

cond-mat.stat-mech↗

arXiv1998

Slow Forcing in the Projective Dynamics Method

We provide a proof that when there is no forcing the recently introduced projective dynamics Monte Carlo algorithm gives the exact lifetime of the metastable state, within statistical uncertainties. We also show numerical evidence illustrating that for slow forcing the approach to the zero-forcing limit is rather rapid. The model studied numerically is the 3-dimensional 3-state Potts ferromagnet.

cond-mat.mtrl-sci↗

arXiv1998

Kinetic Ising model in an oscillating field: Finite-size scaling at the dynamic phase transition

We study hysteresis for a two-dimensional, spin-1/2, nearest-neighbor, kinetic Ising ferromagnet in an oscillating field, using Monte Carlo simulations. The period-averaged magnetization is the order parameter for a proposed dynamic phase transition (DPT). To quantify the nature of this transition, we present the first finite-size scaling study of the DPT for this model. Evidence of a diverging correlation length is given, and we provide estimates of the transition frequency and the critical indices $β$, $γ$ and $ν$.

cond-mat.stat-mech↗

arXiv1998

Magnetic Particles

We present an overview of the subject of Magnetic Particles, starting at a level suitable for advanced high-school students and ending at a level suitable for current practitioners in the field. The sub-topics covered include: Types of Magnetic Materials, Relationships Between the Vector Fields, Magnetic Energies, Dynamics of Magnetic Particles, and Magnetocaloric Effects.

cond-mat.mtrl-sci↗

arXiv1998

Computer Simulations of Thermal Switching in Small-grain Ferromagnets

We present Monte Carlo and Langevin micromagnetic calculations to investigate thermal switching of single-domain ferromagnetic particles. For the Monte Carlo study we place particular emphasis on the probability that the magnetization does not switch by time t. We find that this quantity has different behaviors in different regimes of applied field, temperature, and system size, and we explain this in terms of different reversal mechanisms that dominate in the different regimes. In the micromagnetic study of an array of Ni pillars, we show that the reversal mode is an outside-in mode starting at the perimeter of the array of pillars.

cond-mat.mtrl-sci↗

arXiv1998

A projection method for statics and dynamics of lattice spin systems

A method based on Monte Carlo sampling of the probability flows projected onto the subspace of one or more slow variables is proposed for investigation of dynamic and static properties of lattice spin systems. We illustrate the method by applying it, with projection onto the order-parameter subspace, to the three-dimensional 3-state Potts model in equilibrium and to metastable decay in a three-dimensional 3-state kinetic Potts model.

cond-mat↗

arXiv1998

Hard Simulation Problems in the Modeling of Magnetic Materials: Parallelization and Langevin Micromagnetics

We present recent results on two attempts at understanding and utilizing large-scale simulations of magnetic materials. In the first study we consider massively parallel implementations on a Cray T3E of the n-fold way algorithm for magnetization switching in kinetic Ising models. We find an intricate relationship between the average time increment and the size of the spin blocks on each processor. This narrows the regime of efficient implementation. The second study concerns incorporating noise into micromagnetic calculations using Langevin methods. This allows measurement of quantities such as the probability that the system has not switched within a given time. Preliminary results are reported for arrays of single-domain nanoscale pillars.

cond-mat.mtrl-sci↗

arXiv1998

Stochastic Hysteresis and Resonance in a Kinetic Ising System

We study hysteresis for a two-dimensional, spin-1/2, nearest-neighbor, kinetic Ising ferromagnet in an oscillating field, using Monte Carlo simulations and analytical theory. Attention is focused on small systems and weak field amplitudes at a temperature below $T_{c}$. For these restricted parameters, the magnetization switches through random nucleation of a single droplet of spins aligned with the applied field. We analyze the stochastic hysteresis observed in this parameter regime, using time-dependent nucleation theory and the theory of variable-rate Markov processes. The theory enables us to accurately predict the results of extensive Monte Carlo simulations, without the use of any adjustable parameters. The stochastic response is qualitatively different from what is observed, either in mean-field models or in simulations of larger spatially extended systems. We consider the frequency dependence of the probability density for the hysteresis-loop area and show that its average slowly crosses over to a logarithmic decay with frequency and amplitude for asymptotically low frequencies. Both the average loop area and the residence-time distributions for the magnetization show evidence of stochastic resonance. We also demonstrate a connection between the residence-time distributions and the power spectral densities of the magnetization time series. In addition to their significance for the interpretation of recent experiments in condensed-matter physics, including studies of switching in ferromagnetic and ferroelectric nanoparticles and ultrathin films, our results are relevant to the general theory of periodically driven arrays of coupled, bistable systems with stochastic noise.

cond-mat.mtrl-sci↗

arXiv1998

Hysteresis loop areas in kinetic Ising models: Effects of the switching mechanism

Experiments on ferromagnetic thin films have measured the dependence of the hysteresis loop area on the amplitude and frequency of the external field, $A$=$A(H_{0},ω)$, and approximate agreement with numerical simulations of Ising models has been reported. Here we present numerical and theoretical calculations of $A$ in the low-frequency regime for two values of $H_{0}$, which bracket a temperature and system-size dependent crossover field. Our previous Monte Carlo studies have shown that the hysteretic response of the kinetic Ising model is qualitatively different for amplitudes above and below this crossover field. Using droplet theory, we derive analytic expressions for the low-frequency asymptotic behavior of the hysteresis loop area. In both field regimes, the loop area exhibits an extremely slow approach to an asymptotic, logarithmic frequency dependence of the form $A \propto - [\ln (H_{0} ω)]^{-1}$. Our results are relevant to the interpretation of data from experiments and simulations, on the basis of which power-law exponents for the hysteresis-loop area have been reported.

cond-mat.mtrl-sci↗