1,126 research outputs found
Multicanonical Methods vs. Molecular Dynamics vs. Monte Carlo: Comparison for Lennard-Jones Glasses
We applied a multicanonical algorithm (entropic sampling) to a
two-dimensional and a three-dimensional Lennard-Jones system with
quasicrystalline and glassy ground states. Focusing on the ability of the
algorithm to locate low lying energy states, we compared the results of the
multicanonical simulations with standard Monte Carlo simulated annealing and
molecular dynamics methods. We find slight benefits to using entropic sampling
in small systems (less than 80 particles), which disappear with larger systems.
This is disappointing as the multicanonical methods are designed to surmount
energy barriers to relaxation. We analyze this failure theoretically, and show
(1) the multicanonical method is reduced in the thermodynamic limit (large
systems) to an effective Monte Carlo simulated annealing with a random
temperature vs. time, and (2) the multicanonical method gets trapped by
unphysical entropy barriers in the same metastable states whose energy barriers
trap the traditional quenches. The performance of Monte Carlo and molecular
dynamics quenches were remarkably similar.Comment: 12 pages, 6 figures, REVTEX, epsf.st
Application of Multicanonical Multigrid Monte Carlo Method to the Two-Dimensional -Model: Autocorrelations and Interface Tension
We discuss the recently proposed multicanonical multigrid Monte Carlo method
and apply it to the scalar -model on a square lattice. To investigate
the performance of the new algorithm at the field-driven first-order phase
transitions between the two ordered phases we carefully analyze the
autocorrelations of the Monte Carlo process. Compared with standard
multicanonical simulations a real-time improvement of about one order of
magnitude is established. The interface tension between the two ordered phases
is extracted from high-statistics histograms of the magnetization applying
histogram reweighting techniques.Comment: 49 pp. Latex incl. 14 figures (Fig.7 not included, sorry) as
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Multicanonical Monte Carlo Calculation of the First-order Phase Transition of Lennard-Jones Fluids
The liquid-solid phase transition was investigated by the multicanonical Monte Carlo method for a bulk Lennard-Jones fluid system that consists of 256 argon particles. The reliability of the multicanonical weight factor we determined was confirmed by the flatness of the histogram obtained by the multicanonical Monte Carlo production run. The first-order phase transition between solid and liquid phase was observed around 130 K from the change in thermodynamic properties as a function of temperature. Besides, the small change between two solid structures was also observed at 60 K from the radial distribution function, from the heat capacity and from conventional canonical Monte Carlo calculation at 60 K. Neither of them is not f. c. c. structure which is known as the most stable
Simulation of Lattice Polymers with Multi-Self-Overlap Ensemble
A novel family of dynamical Monte Carlo algorithms for lattice polymers is
proposed. Our central idea is to simulate an extended ensemble in which the
self-avoiding condition is systematically weakened. The degree of the
self-overlap is controlled in a similar manner as the multicanonical ensemble.
As a consequence, the ensemble --the multi-self-overlap ensemble-- contains
adequate portions of self-overlapping conformations as well as higher energy
ones. It is shown that the multi-self-overlap ensemble algorithm reproduce
correctly the canonical averages at finite temperatures of the HP model of
lattice proteins. Moreover, it outperforms massively a standard multicanonical
algorithm for a difficult example of a polymer with 8-stickers. Alternative
algorithm based on exchange Monte Carlo method is also discussed.Comment: 5 Pages, 4 Postscript figures, uses epsf.st
Multicanonical Parallel Tempering
We present a novel implementation of the parallel tempering Monte Carlo
method in a multicanonical ensemble. Multicanonical weights are derived by a
self-consistent iterative process using a Boltzmann inversion of global energy
histograms. This procedure gives rise to a much broader overlap of
thermodynamic-property histograms; fewer replicas are necessary in parallel
tempering simulations, and the acceptance of trial swap moves can be made
arbitrarily high. We demonstrate the usefulness of the method in the context of
a grand-multicanonical ensemble, where we use multicanonical simulations in
energy space with the addition of an unmodified chemical potential term in
particle-number space. Several possible implementations are discussed, and the
best choice is presented in the context of the liquid-gas phase transition of
the Lennard-Jones fluid. A substantial decrease in the necessary number of
replicas can be achieved through the proposed method, thereby providing a
higher efficiency and the possibility of parallelization.Comment: 8 pages, 3 figure, accepted by J Chem Phy
Combination of improved multibondic method and the Wang-Landau method
We propose a method for Monte Carlo simulation of statistical physical models
with discretized energy. The method is based on several ideas including the
cluster algorithm, the multicanonical Monte Carlo method and its acceleration
proposed recently by Wang and Landau. As in the multibondic ensemble method
proposed by Janke and Kappler, the present algorithm performs a random walk in
the space of the bond population to yield the state density as a function of
the bond number. A test on the Ising model shows that the number of Monte Carlo
sweeps required of the present method for obtaining the density of state with a
given accuracy is proportional to the system size, whereas it is proportional
to the system size squared for other conventional methods. In addition, the new
method shows a better performance than the original Wang-Landau method in
measurement of physical quantities.Comment: 12 pages, 3 figure
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