331 research outputs found
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
-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
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