15,398 research outputs found
Exchange Monte Carlo Method and Application to Spin Glass Simulations
We propose an efficient Monte Carlo algorithm for simulating a
``hardly-relaxing" system, in which many replicas with different temperatures
are simultaneously simulated and a virtual process exchanging configurations of
these replica is introduced. This exchange process is expected to let the
system at low temperatures escape from a local minimum. By using this algorithm
the three-dimensional Ising spin glass model is studied. The ergodicity
time in this method is found much smaller than that of the multi-canonical
method. In particular the time correlation function almost follows an
exponential decay whose relaxation time is comparable to the ergodicity time at
low temperatures. It suggests that the system relaxes very rapidly through the
exchange process even in the low temperature phase.Comment: 10 pages + uuencoded 5 Postscript figures, REVTe
Multicanonical Recursions
The problem of calculating multicanonical parameters recursively is
discussed. I describe in detail a computational implementation which has worked
reasonably well in practice.Comment: 23 pages, latex, 4 postscript figures included (uuencoded
Z-compressed .tar file created by uufiles), figure file corrected
Simulated-tempering approach to spin-glass simulations
After developing an appropriate iteration procedure for the determination of
the parameters, the method of simulated tempering has been successfully applied
to the 2D Ising spin glass. The reduction of the slowing down is comparable to
that of the multicanonical algorithm. Simulated tempering has, however, the
advantages to allow full vectorization of the programs and to provide the
canonical ensemble directly.Comment: 12 pages (LaTeX), 4 postscript figures, uufiles encoded, submitted to
Physical Review
Grundstate Properties of the 3D Ising Spin Glass
We study zero--temperature properties of the 3d Edwards--Anderson Ising spin
glass on finite lattices up to size . Using multicanonical sampling we
generate large numbers of groundstate configurations in thermal equilibrium.
Finite size scaling with a zero--temperature scaling exponent describes the data well. Alternatively, a descriptions in terms of Parisi
mean field behaviour is still possible. The two scenarios give significantly
different predictions on lattices of size .Comment: LATEX 9pages,figures upon request ,SCRI-9
Spin glass overlap barriers in three and four dimensions
For the Edwards-Anderson Ising spin-glass model in three and four dimensions
(3d and 4d) we have performed high statistics Monte Carlo calculations of those
free-energy barriers which are visible in the probability density
of the Parisi overlap parameter . The calculations rely on the
recently introduced multi-overlap algorithm. In both dimensions, within the
limits of lattice sizes investigated, these barriers are found to be
non-self-averaging and the same is true for the autocorrelation times of our
algorithm. Further, we present evidence that barriers hidden in dominate
the canonical autocorrelation times.Comment: 20 pages, Latex, 12 Postscript figures, revised version to appear in
Phys. Rev.
Extending the functionalities of shear-driven chromatography nano-channels using high aspect ratio etching
An new injection system is presented for shear-driven chromatography. The device has been fabricated by high aspect ratio etching of silicon. The performance of the injection slit is studied through the aid of computational fluid dynamics, and the first experimental results are presented
Analysis of existing mathematics textbooks for use in secondary schools.
Thesis (Ed.M.)--Boston University
Thesis (M.A.)--Boston Universit
Monte Carlo simulation and global optimization without parameters
We propose a new ensemble for Monte Carlo simulations, in which each state is
assigned a statistical weight , where is the number of states with
smaller or equal energy. This ensemble has robust ergodicity properties and
gives significant weight to the ground state, making it effective for hard
optimization problems. It can be used to find free energies at all temperatures
and picks up aspects of critical behaviour (if present) without any parameter
tuning. We test it on the travelling salesperson problem, the Edwards-Anderson
spin glass and the triangular antiferromagnet.Comment: 10 pages with 3 Postscript figures, to appear in Phys. Rev. Lett
Transition matrix Monte Carlo method for quantum systems
We propose an efficient method for Monte Carlo simulation of quantum lattice
models. Unlike most other quantum Monte Carlo methods, a single run of the
proposed method yields the free energy and the entropy with high precision for
the whole range of temperature. The method is based on several recent findings
in Monte Carlo techniques, such as the loop algorithm and the transition matrix
Monte Carlo method. In particular, we derive an exact relation between the DOS
and the expectation value of the transition probability for quantum systems,
which turns out to be useful in reducing the statistical errors in various
estimates.Comment: 6 pages, 4 figure
- …