Low-Temperature Long-Time Simulations of Ising Ferromagnets using the Monte Carlo with Absorbing Markov Chains method

The Monte Carlo with Absorbing Markov Chains (MCAMC) method is introduced. This method is a generalization of the rejection-free method known as the $n$-fold way. The MCAMC algorithm is applied to the study of the very low-temperature properties of the lifetime of the metastable state of Ising ferromagnets. This is done both for square-lattice and cubic-lattice nearest-neighbor models. Comparison is made with exact low-temperature predictions, in particular the low-temperature predictions that the metastable lifetime is discontinuous at particular values of the field. This discontinuity for the square lattice is not seen in finite-temperatures studies. For the cubic lattice, it is shown that these `exact predictions' are incorrect near the fields where there are discontinuities. The low-temperature formula must be modified and the corrected low-temperature predictions are not discontinuous in the energy of the nucleating droplet.Comment: Submitted to Computer Physics Communicatinos, for proceedings of the Conference CCP2001, 4 figure

Rejection-free Monte Carlo Algorithms for Models with Continuous Degrees of Freedom

We construct a rejection-free Monte Carlo algorithm for a system with continuous degrees of freedom. We illustrate the algorithm by applying it to the classical three-dimensional Heisenberg model with canonical Metropolis dynamics. We obtain the lifetime of the metastable state following a reversal of the external magnetic field. Our rejection-free algorithm obtains results in agreement with a direct implementation of the Metropolis dynamic and requires orders of magnitude less computational time at low temperatures. The treatment is general and can be extended to other dynamics and other systems with continuous degrees of freedom.Comment: 4 pages, including figures. PRE, in pres

Efficiencies of dynamic Monte Carlo algorithms for off-lattice particle systems with a single impurity

AbstractThe efficiency of dynamic Monte Carlo algorithms for off-lattice systems composed of particles is studied for the case of a single impurity particle. The theoretical efficiencies of the rejection-free method and of the Monte Carlo with Absorbing Markov Chains method are given. Simulation results are presented to confirm the theoretical efficiencies

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.Comment: 17 pages, 7 figures, RevTex; submitted to the Journal of Computational Physic

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.Comment: 14 pages, 4 figures, submitted to J. Non-Crystalline Solids, conference proceeding for IXth International Conference on the Physics of Non-Crystalline Solids, October, 199

Magnetization Switching in Single-Domain Ferromagnets

A model for single-domain uniaxial ferromagnetic particles with high anisotropy, the Ising model, is studied. Recent experimental observations have been made of the probability that the magnetization has not switched. Here an approach is described in which it is emphasized that a ferromagnetic particle in an unfavorable field is in fact a metastable system, and the switching is accomplished through the nucleation and subsequent growth of localized droplets. Nucleation theory is applied to finite systems to determine the coercivity as a function of particle size and to calculate the probability of not switching. Both of these quantities are modified by different boundary conditions, magnetostatic interactions, and quenched disorder.Comment: 4 pages, LaTeX, 2 figures, documentstyle{elsart} More fits and Mathematica notebook at http://www.scri.fsu.edu/~novotny/magnetism.html To appear in J.Mag.Mag.Mater. Conference Proceedings of 7th International Conference on Magnetism Cairns, Australia, August, 199

Microstructure and velocity of field-driven Ising interfaces moving under a soft stochastic dynamic

We present theoretical and dynamic Monte Carlo simulation results for the mobility and microscopic structure of 1+1-dimensional Ising interfaces moving far from equilibrium in an applied field under a single-spin-flip ``soft'' stochastic dynamic. The soft dynamic is characterized by the property that the effects of changes in field energy and interaction energy factorize in the transition rate, in contrast to the nonfactorizing nature of the traditional Glauber and Metropolis rates (``hard'' dynamics). This work extends our previous studies of the Ising model with a hard dynamic and the unrestricted SOS model with soft and hard dynamics. [P.A. Rikvold and M. Kolesik, J. Stat. Phys. 100, 377 (2000); J. Phys. A 35, L117 (2002); Phys. Rev. E 66, 066116 (2002).] The Ising model with soft dynamics is found to have closely similar properties to the SOS model with the same dynamic. In particular, the local interface width does not diverge with increasing field, as it does for hard dynamics. The skewness of the interface at nonzero field is very weak and has the opposite sign of that obtained with hard dynamics.Comment: 19 pages LaTex with 7 imbedded figure