1,775 research outputs found
Wang-Landau sampling for quantum systems: algorithms to overcome tunneling problems and calculate the free energy
We present a generalization of the classical Wang-Landau algorithm [Phys.
Rev. Lett. 86, 2050 (2001)] to quantum systems. The algorithm proceeds by
stochastically evaluating the coefficients of a high temperature series
expansion or a finite temperature perturbation expansion to arbitrary order.
Similar to their classical counterpart, the algorithms are efficient at thermal
and quantum phase transitions, greatly reducing the tunneling problem at first
order phase transitions, and allow the direct calculation of the free energy
and entropy.Comment: Added a plot showing the efficiency at first order phase transition
Configurational entropy of Wigner crystals
We present a theoretical study of classical Wigner crystals in two- and
three-dimensional isotropic parabolic traps aiming at understanding and
quantifying the configurational uncertainty due to the presence of multiple
stable configurations. Strongly interacting systems of classical charged
particles confined in traps are known to form regular structures. The number of
distinct arrangements grows very rapidly with the number of particles, many of
these arrangements have quite low occurrence probabilities and often the
lowest-energy structure is not the most probable one. We perform numerical
simulations on systems containing up to 100 particles interacting through
Coulomb and Yukawa forces, and show that the total number of metastable
configurations is not a well defined and representative quantity. Instead, we
propose to rely on the configurational entropy as a robust and objective
measure of uncertainty. The configurational entropy can be understood as the
logarithm of the effective number of states; it is insensitive to the presence
of overlooked low-probability states and can be reliably determined even within
a limited time of a simulation or an experiment.Comment: 12 pages, 8 figures. This is an author-created, un-copyedited version
of an article accepted for publication in J. Phys.: Condens. Matter. IOP
Publishing Ltd is not responsible for any errors or omissions in this version
of the manuscript or any version derived from it. The definitive
publisher-authenticated version is available online at
10.1088/0953-8984/23/7/075302.
Parallelization of Markov chain generation and its application to the multicanonical method
We develop a simple algorithm to parallelize generation processes of Markov
chains. In this algorithm, multiple Markov chains are generated in parallel and
jointed together to make a longer Markov chain. The joints between the
constituent Markov chains are processed using the detailed balance. We apply
the parallelization algorithm to multicanonical calculations of the
two-dimensional Ising model and demonstrate accurate estimation of
multicanonical weights.Comment: 15 pages, 5 figures, uses elsart.cl
Monte Carlo approach of the islanding of polycrystalline thin films
We computed by a Monte Carlo method derived from the Solid on Solid model,
the evolution of a polycrystalline thin film deposited on a substrate during
thermal treatment. Two types of substrates have been studied: a single
crystalline substrate with no defects and a single crystalline substrate with
defects. We obtain islands which are either flat (i.e. with a height which does
not overcome a given value) or grow in height like narrow towers. A good
agreement was found regarding the morphology of numerical nanoislands at
equilibrium, deduced from our model, and experimental nanoislands resulting
from the fragmentation of YSZ thin films after thermal treatment.Comment: 20 pages, 7 figure
Projected single-spin flip dynamics in the Ising Model
We study transition matrices for projected dynamics in the
energy-magnetization space, magnetization space and energy space. Several
single spin flip dynamics are considered such as the Glauber and Metropolis
canonical ensemble dynamics and the Metropolis dynamics for three
multicanonical ensembles: the flat energy-magnetization histogram, the flat
energy histogram and the flat magnetization histogram. From the numerical
diagonalization of the matrices for the projected dynamics we obtain the
sub-dominant eigenvalue and the largest relaxation times for systems of varying
size. Although, the projected dynamics is an approximation to the full state
space dynamics comparison with some available results, obtained by other
authors, shows that projection in the magnetization space is a reasonably
accurate method to study the scaling of relaxation times with system size. The
transition matrices for arbitrary single-spin flip dynamics are obtained from a
single Monte-Carlo estimate of the infinite temperature transition-matrix, for
each system size, which makes the method an efficient tool to evaluate the
relative performance of any arbitrary local spin-flip dynamics. We also present
new results for appropriately defined average tunnelling times of magnetization
and compute their finite-size scaling exponents that we compare with results of
energy tunnelling exponents available for the flat energy histogram
multicanonical ensemble.Comment: 23 pages and 6 figure
Lattice QCD and the Schwarz alternating procedure
A numerical simulation algorithm for lattice QCD is described, in which the
short- and long-distance effects of the sea quarks are treated separately. The
algorithm can be regarded, to some extent, as an implementation at the quantum
level of the classical Schwarz alternating procedure for the solution of
elliptic partial differential equations. No numerical tests are reported here,
but theoretical arguments suggest that the algorithm should work well also at
small quark masses.Comment: Plain TeX source, 20 pages, figures include
Dielectric susceptibility of the Coulomb-glass
We derive a microscopic expression for the dielectric susceptibility
of a Coulomb glass, which corresponds to the definition used in classical
electrodynamics, the derivative of the polarization with respect to the
electric field. The fluctuation-dissipation theorem tells us that is a
function of the thermal fluctuations of the dipole moment of the system. We
calculate numerically for three-dimensional Coulomb glasses as a
function of temperature and frequency
Monte Carlo Study of the Separation of Energy Scales in Quantum Spin 1/2 Chains with Bond Disorder
One-dimensional Heisenberg spin 1/2 chains with random ferro- and
antiferromagnetic bonds are realized in systems such as . We have investigated numerically the thermodynamic properties of a
generic random bond model and of a realistic model of by the quantum Monte Carlo loop algorithm. For the first time we
demonstrate the separation into three different temperature regimes for the
original Hamiltonian based on an exact treatment, especially we show that the
intermediate temperature regime is well-defined and observable in both the
specific heat and the magnetic susceptibility. The crossover between the
regimes is indicated by peaks in the specific heat. The uniform magnetic
susceptibility shows Curie-like behavior in the high-, intermediate- and
low-temperature regime, with different values of the Curie constant in each
regime. We show that these regimes are overlapping in the realistic model and
give numerical data for the analysis of experimental tests.Comment: 7 pages, 5 eps-figures included, typeset using JPSJ.sty, accepted for
publication in J. Phys. Soc. Jpn. 68, Vol. 3. (1999
Monte Carlo Procedure for Protein Design
A new method for sequence optimization in protein models is presented. The
approach, which has inherited its basic philosophy from recent work by Deutsch
and Kurosky [Phys. Rev. Lett. 76, 323 (1996)] by maximizing conditional
probabilities rather than minimizing energy functions, is based upon a novel
and very efficient multisequence Monte Carlo scheme. By construction, the
method ensures that the designed sequences represent good folders
thermodynamically. A bootstrap procedure for the sequence space search is
devised making very large chains feasible. The algorithm is successfully
explored on the two-dimensional HP model with chain lengths N=16, 18 and 32.Comment: 7 pages LaTeX, 4 Postscript figures; minor change
Probing a non-biaxial behavior of infinitely thin hard platelets
We give a criterion to test a non-biaxial behavior of infinitely thin hard
platelets of symmetry based upon the components of three order
parameter tensors. We investigated the nematic behavior of monodisperse
infinitely thin rectangular hard platelet systems by using the criterion.
Starting with a square platelet system, and we compared it with rectangular
platelet systems of various aspect ratios. For each system, we performed
equilibration runs by using isobaric Monte Carlo simulations. Each system did
not show a biaxial nematic behavior but a uniaxial nematic one, despite of the
shape anisotropy of those platelets. The relationship between effective
diameters by simulations and theoretical effective diameters of the above
systems was also determined.Comment: Submitted to JPS
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