arXiv subjects

M. A. Novotny

Publications and source records attributed to M. A. Novotny.

At least 37 records · Page 2Linked to original sources

arXiv2008

Resolution-dependent mechanisms for bimodal switching-time distributions in simulated Fe nanopillars

We study the magnetization-switching statistics following reversal of the applied field for three separate computational models representing the same physical system, an iron nanopillar. The primary difference between the models is the resolution of the computational lattice and, consequently, the intrinsic parameters that must be rescaled to retain similarity to the physical system. Considering the first-passage time to zero for the magnetization component in the longitudinal (easy-axis) direction, we look for applied fields that result in bimodal distributions of this time for each system and compare the results to the experimental system. We observe that the relevant fluctuations leading to bimodal distributions are different for each lattice resolution and result in magnetization-switching behavior that is unique to each computational model. Correct model resolution is thus essential for obtaining reliable numerical results for the system dynamics.

cond-mat.mtrl-sci↗

arXiv2008

Evidence for a dynamic phase transition in [Co/Pt]_3 magnetic multilayers

A dynamic phase transition (DPT) with respect to the period P of an applied alternating magnetic field has been observed previously in numerical simulations of magnetic systems. However, experimental evidence for this DPT has thus far been limited to qualitative observations of hysteresis loop collapse in studies of hysteresis loop area scaling. Here, we present significantly stronger evidence for the experimental observation of this DPT, in a [Co(4 A)/Pt(7 A)]_3-multilayer system with strong perpendicular anisotropy. We applied an out-of-plane, time-varying (sawtooth) field to the [Co/Pt]_3 multilayer, in the presence of a small additional constant field, H_b. We then measured the resulting out-of-plane magnetization time series to produce nonequilibrium phase diagrams (NEPDs) of the cycle-averaged magnetization, Q, and its variance, Var(Q), as functions of P and H_b. The experimental NEPDs are found to strongly resemble those calculated from simulations of a kinetic Ising model under analagous conditions. The similarity of the experimental and simulated NEPDs, in particular the presence of a localized peak in the variance Var(Q) in the experimental results, constitutes strong evidence for the presence of this DPT in our magnetic multilayer samples. Technical challenges related to the hysteretic nature and response time of the electromagnet used to generate the time-varying applied field precluded us from extracting meaningful critical scaling exponents from the current data. However, based on our results, we propose refinements to the experimental procedure which could potentially enable the determination of critical exponents in the future.

cond-mat.stat-mech↗

arXiv2007

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 for the first time 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, δ_d, of H_b at the critical period of the DPT is equal to the exponent for the critical isotherm, δ_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, H_0) 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 / \partial H_b, in the critical region.

cond-mat.stat-mech↗

arXiv2007

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 bi-modal 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 $T = 20$ K and the reversal field 3160 Oe at an angle of 75$^\circ$ to the long axis, approximately 70% of the switches involve unstable decay (no free-energy barrier) and 30% involve metastable decay (a free-energy barrier is crossed). The latter are indistinguishable from switches which are constrained to start at a metastable free-energy minimum. Competition between unstable and metastable decay could greatly complicate applications involving magnetization switches near the coercive field.

cond-mat.stat-mech↗

arXiv2007

Nanostructure and velocity of field-driven solid-on-solid interfaces moving under a phonon-assisted dynamic

The nanoscopic structure and the stationary propagation velocity of (1+1)-dimensional solid-on-solid interfaces in an Ising lattice-gas model, which are driven far from equilibrium by an applied force, such as a magnetic field or a difference in (electro)chemical potential, are studied by an analytic nonlinear-response approximation together with kinetic Monte Carlo simulations. Here we consider the case that the system is coupled to a two-dimensional phonon bath. In the resulting dynamic, transitions that conserve the system energy are forbidden, and the effects of the applied force and the interaction energies do not factorize (a so-called hard dynamic). In full agreement with previous general theoretical results we find that the local interface width changes dramatically with the applied force. However, in contrast with other hard dynamics, this change is nonmonotonic in the driving force. However, significant differences between theory and simulation are found near two special values of the driving force, where certain transitions allowed by the solid-on-solid model become forbidden by the phonon-assisted dynamic. Our results represent a significant step toward providing a solid physical foundation for kinetic Monte Carlo simulations.

cond-mat.stat-mech↗

arXiv2006

A rejection-free Monte Carlo method for the hard-disk system

We construct a rejection-free Monte Carlo method for the hard-disk system. Rejection-free Monte Carlo methods preserve the time-evolution behavior of the standard Monte Carlo method, and this relationship is confirmed for our method by observing nonequilibrium relaxation of a bond-orientational order parameter. The rejection-free method gives a greater computational efficiency than the standard method at high densities. The rejection free method is implemented in a shrewd manner using optimization methods to calculate a rejection probability and to update the system. This method should allow an efficient study of the dynamics of two-dimensional solids at high density.

cond-mat.stat-mech↗

arXiv2006

Subclasses in Mixing Correlated Growth Processes with Randomness

We show that in the construction of continuum equations for competitive growth processes that are a mixture of random deposition and a correlation process, a distinction must be made within a \textit{single universality class} between depositions that do and do not create voids in the bulk. Within these subclasses the bulk morphology is reflected in the surface roughening via \textit{nonuniversal} prefactors in the universal scaling of the surface width.

cond-mat.stat-mech↗

arXiv2006

Finite-temperature Simulations for Magnetic Nanostructures

We examine different models and methods for studying finite-temperature magnetic hysteresis in nanoparticles and ultrathin films. This includes micromagnetic results for the hysteresis of a single magnetic nanoparticle which is misaligned with respect to the magnetic field. We present results from both a representation of the particle as a one-dimensional array of magnetic rotors, and from full micromagnetic simulations. The results are compared with the Stoner-Wohlfarth model. Results of kinetic Monte Carlo simulations of ultrathin films are also presented. In addition, we discuss other topics of current interest in the modeling of magnetic hysteresis in nanostructures, including kinetic Monte Carlo simulations of dynamic phase transitions and First-Order Reversal Curves.

cond-mat.mtrl-sci↗

arXiv2006

Monte Carlo Simulation of Small-World Models with Weak Long-Range Interactions

Large-scale Monte Carlo simulations, together with scaling, are used to obtain the critical behavior of the Hastings long-range model and two corresponding models based on small-world networks. These models have combined short- and long-range interactions. For all three models, the critical scaling behavior predicted by Hastings [Phys. Rev. Lett. 91, 098701] is verified.

cond-mat.mtrl-sci↗

arXiv2006

Synchronization Landscapes in Small-World-Connected Computer Networks

Motivated by a synchronization problem in distributed computing we studied a simple growth model on regular and small-world networks, embedded in one and two-dimensions. We find that the synchronization landscape (corresponding to the progress of the individual processors) exhibits Kardar-Parisi-Zhang-like kinetic roughening on regular networks with short-range communication links. Although the processors, on average, progress at a nonzero rate, their spread (the width of the synchronization landscape) diverges with the number of nodes (desynchronized state) hindering efficient data management. When random communication links are added on top of the one and two-dimensional regular networks (resulting in a small-world network), large fluctuations in the synchronization landscape are suppressed and the width approaches a finite value in the large system-size limit (synchronized state). In the resulting synchronization scheme, the processors make close-to-uniform progress with a nonzero rate without global intervention. We obtain our results by ``simulating the simulations", based on the exact algorithmic rules, supported by coarse-grained arguments.

cond-mat.stat-mech↗

arXiv2005

Universal Scaling in Mixing Correlated Growth with Randomness

We study two-component growth that mixes random deposition (RD) with a correlated growth process that occurs with probability p. We find that these composite systems are in the universality class of the correlated growth process. For RD blends with either Edwards-Wilkinson of Kardar-Parisi-Zhang processes, we identify a nonuniversal parameter in the universal scaling in p.

cond-mat.mtrl-sci↗

arXiv2004

FORC Analysis of homogeneous nucleation in the two-dimensional kinetic Ising model

The first-order reversal curve (FORC) method is applied to the two-dimensional kinetic Ising model. For the system size and magnetic field chosen, the system reverses by the homogeneous nucleation and growth of many droplets. This makes the dynamics of reversal nearly deterministic, in contrast to the strongly disordered systems previously studied by the FORC method. Consequently, the FORC diagrams appear different from those obtained in previous studies. The Kolmogorov-Johnson-Mehl-Avrami (KJMA) theory of phase transformation by nucleation and growth is applied to the system. Reasonable agreement with the Monte Carlo simulations is found, and the FORC method suggests how the KJMA theory could be extended.

cond-mat.stat-mech↗

arXiv2004

Magnetic Small World Nanomaterials: Physical Small World Networks

The question addressed is whether magnetic materials based on physical small world networks are possible. Physical constraints, such as uniform bond length and embedding in three dimensions, are the new features added to make small world networks physical. Results are presented to further determine if physical small world networks can exist, and the effect of the small world connections on the critical phenomena of Ising models on such networks. Spectra of the Laplacian on randomly-collapsed bead-chain networks are studied. The scaling function for the order parameter of an Ising model with physical small world connections is presented.

cond-mat.mtrl-sci↗

arXiv2004

Desynchronization and Speedup in an Asynchronous Conservative Parallel Update Protocol

In a state-update protocol for a system of $L$ asynchronous parallel processes that communicate only with nearest neighbors, global desynchronization in operation times can be deduced from kinetic roughening of the corresponding virtual-time horizon (VTH). The utilization of the parallel processing environment can be deduced by analyzing the microscopic structure of the VTH. We give an overview of how the methods of non-equilibrium surface growth (physics of complex systems) can be applied to uncover some properties of state update algorithms used in distributed parallel discrete-event simulations (PDES). In particular, we focus on the asynchronous conservative PDES algorithm in a ring communication topology. The time evolution of its VTH is simulated numerically as asynchronous cellular automaton whose update rule corresponds to the update rule followed by this algorithm. We give theoretical estimates of the performance as a function of $L$ and the load per processor, i.e., approximate formulas for the mean speedup and for the desynchronization. It is established that, for a given simulation size, there is a theoretical upper bound for the desynchronization and a theoretical non-zero lower bound for the utilization. The new approach to performance studies, outlined in this chapter, is particularly useful in the search for the design of a new-generation of algorithms that would efficiently carry out an autonomous or tunable synchronization.

cs.DC↗

arXiv2004

Roughening of the (1+1) interfaces in two-component surface growth with an admixture of random deposition

We simulate competitive two-component growth on a one dimensional substrate of $L$ sites. One component is a Poisson-type deposition that generates Kardar-Parisi-Zhang (KPZ) correlations. The other is random deposition (RD). We derive the universal scaling function of the interface width for this model and show that the RD admixture acts as a dilatation mechanism to the fundamental time and height scales, but leaves the KPZ correlations intact. This observation is generalized to other growth models. It is shown that the flat-substrate initial condition is responsible for the existence of an early non-scaling phase in the interface evolution. The length of this initial phase is a non-universal parameter, but its presence is universal. In application to parallel and distributed computations, the important consequence of the derived scaling is the existence of the upper bound for the desynchronization in a conservative update algorithm for parallel discrete-event simulations. It is shown that such algorithms are generally scalable in a ring communication topology.

cond-mat.mtrl-sci↗

arXiv2004

Low-temperature nucleation in a kinetic Ising model under different stochastic dynamics with local energy barriers

Using both analytical and simulational methods, we study low-temperature nucleation rates in kinetic Ising lattice-gas models that evolve under two different Arrhenius dynamics that interpose between the Ising states a transition state representing a local energy barrier. The two dynamics are the transition-state approximation [T. Ala-Nissila, J. Kjoll, and S. C. Ying, Phys. Rev. B 46, 846 (1992)] and the one-step dynamic [H. C. Kang and W. H. Weinberg, J. Chem. Phys. 90, 2824 (1989)]. Even though they both obey detailed balance and are here applied to a situation that does not conserve the order parameter, we find significant differences between the nucleation rates observed with the two dynamics, and between them and the standard Glauber dynamic [R. J. Glauber, J. Math. Phys. 4, 294 (1963)], which does not contain transition states. Our results show that great care must be exercised when devising kinetic Monte Carlo transition rates for specific physical or chemical systems.

cond-mat.stat-mech↗

arXiv2004

Vortex Velocity Probability Distributions in Phase Ordering Kinetics

The calculation of the point vortex velocity probability distribution function (vvpdf) is extended to a larger class of systems beyond the nonconserved TDGL model treated earlier. The range is extended to include certain anisotropic models and the conserved order parameter case. The vvpdf still satisfies scaling with large velocity tails as for the nonconserved isotropic case. It is shown that the average vortex speed can be self-consistently expressed in terms of correlation functions associated with a Gaussian auxiliary field. In the conserved order parameter case the average vortex speed decays as $t^{-1}$ compared to the $t^{-1/2}$ decay for the nonconserved case.

cond-mat.soft↗

arXiv2004

Discrete-Event Analytic Technique for Surface Growth Problems

We introduce an approach for calculating non-universal properties of rough surfaces. The technique uses concepts of distinct surface-configuration classes, defined by the surface growth rule. The key idea is a mapping between discrete events that take place on the interface and its elementary local-site configurations. We construct theoretical probability distributions of deposition events at saturation for surfaces generated by selected growth rules. These distributions are then used to compute measurable physical quantities. Despite the neglect of temporal correlations, our approximate analytical results are in very good agreement with numerical simulations. This discrete-event analytic technique can be particularly useful when applied to quantification problems, which are known to not be suited to continuum methods.

cond-mat.stat-mech↗