186 research outputs found
Multigrid Monte Carlo Algorithms for SU(2) Lattice Gauge Theory: Two versus Four Dimensions
We study a multigrid method for nonabelian lattice gauge theory, the time
slice blocking, in two and four dimensions. For SU(2) gauge fields in two
dimensions, critical slowing down is almost completely eliminated by this
method. This result is in accordance with theoretical arguments based on the
analysis of the scale dependence of acceptance rates for nonlocal Metropolis
updates. The generalization of the time slice blocking to SU(2) in four
dimensions is investigated analytically and by numerical simulations. Compared
to two dimensions, the local disorder in the four dimensional gauge field leads
to kinematical problems.Comment: 24 pages, PostScript file (compressed and uuencoded), preprint
MS-TPI-94-
Logarithmic Corrections in the 2D XY Model
Using two sets of high-precision Monte Carlo data for the two-dimensional XY
model in the Villain formulation on square lattices, the scaling
behavior of the susceptibility and correlation length at the
Kosterlitz-Thouless phase transition is analyzed with emphasis on
multiplicative logarithmic corrections in the finite-size
scaling region and in the high-temperature phase near
criticality, respectively. By analyzing the susceptibility at criticality on
lattices of size up to we obtain , in agreement with
recent work of Kenna and Irving on the the finite-size scaling of Lee-Yang
zeros in the cosine formulation of the XY model. By studying susceptibilities
and correlation lengths up to in the high-temperature phase,
however, we arrive at quite a different estimate of , which is
in good agreement with recent analyses of thermodynamic Monte Carlo data and
high-temperature series expansions of the cosine formulation.Comment: 13 pages, LaTeX + 8 postscript figures. See also
http://www.cond-mat.physik.uni-mainz.de/~janke/doc/home_janke.htm
The Percolation Signature of the Spin Glass Transition
Magnetic ordering at low temperature for Ising ferromagnets manifests itself
within the associated Fortuin-Kasteleyn (FK) random cluster representation as
the occurrence of a single positive density percolating network. In this paper
we investigate the percolation signature for Ising spin glass ordering -- both
in short-range (EA) and infinite-range (SK) models -- within a two-replica FK
representation and also within the different Chayes-Machta-Redner two-replica
graphical representation. Based on numerical studies of the EA model in
three dimensions and on rigorous results for the SK model, we conclude that the
spin glass transition corresponds to the appearance of {\it two} percolating
clusters of {\it unequal} densities.Comment: 13 pages, 6 figure
Reexamination of the long-range Potts model: a multicanonical approach
We investigate the critical behavior of the one-dimensional q-state Potts
model with long-range (LR) interaction , using a multicanonical
algorithm. The recursion scheme initially proposed by Berg is improved so as to
make it suitable for a large class of LR models with unequally spaced energy
levels. The choice of an efficient predictor and a reliable convergence
criterion is discussed. We obtain transition temperatures in the first-order
regime which are in far better agreement with mean-field predictions than in
previous Monte Carlo studies. By relying on the location of spinodal points and
resorting to scaling arguments, we determine the threshold value
separating the first- and second-order regimes to two-digit precision within
the range . We offer convincing numerical evidence supporting
$\sigma_c(q)Comment: 18 pages, 18 figure
Ising model on 3D random lattices: A Monte Carlo study
We report single-cluster Monte Carlo simulations of the Ising model on
three-dimensional Poissonian random lattices with up to 128,000 approx. 503
sites which are linked together according to the Voronoi/Delaunay prescription.
For each lattice size quenched averages are performed over 96 realizations. By
using reweighting techniques and finite-size scaling analyses we investigate
the critical properties of the model in the close vicinity of the phase
transition point. Our random lattice data provide strong evidence that, for the
available system sizes, the resulting effective critical exponents are
indistinguishable from recent high-precision estimates obtained in Monte Carlo
studies of the Ising model and \phi^4 field theory on three-dimensional regular
cubic lattices.Comment: 35 pages, LaTex, 8 tables, 8 postscript figure
Understanding How Inequality in the Distribution of Income Affects Health
Research on the determinants of health has almost exclusively focused on the individual but it seems clear we cannot understand or improve patterns of population health without engaging structural determinants at the societal level. This article traces the development of research on income distribution and health to the most recent epidemiologic studies from the USA that show how income inequality is related to age-adjusted mortality within the 50 States. (r 520.62, p 5 0.0001) even after accounting for absolute levels of income. We discuss potential material, psychological, social and behavioral pathways through which income distribution might be linked to health status. Distributional aspects of the economy are important determinants of health and may well provide one of the most pertinent indicators of overall social well-being.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/66686/2/10.1177_135910539700200303.pd
Cluster Monte Carlo and dynamical scaling for long-range interactions
Many spin systems affected by critical slowing down can be efficiently
simulated using cluster algorithms. Where such systems have long-range
interactions, suitable formulations can additionally bring down the
computational effort for each update from O() to O() or even
O(), thus promising an even more dramatic computational speed-up. Here, we
review the available algorithms and propose a new and particularly efficient
single-cluster variant. The efficiency and dynamical scaling of the available
algorithms are investigated for the Ising model with power-law decaying
interactions.Comment: submitted to Eur. Phys. J Spec. Topic
A Percolation-Theoretic Approach to Spin Glass Phase Transitions
The magnetically ordered, low temperature phase of Ising ferro- magnets is
manifested within the associated Fortuin-Kasteleyn (FK) random cluster
representation by the occurrence of a single positive density percolating
cluster. In this paper, we review our recent work on the percolation signature
for Ising spin glass ordering -- both in the short-range Edwards-Anderson (EA)
and infinite-range Sherrington-Kirkpatrick (SK) models -- within a two-replica
FK representation and also in the different Chayes-Machta-Redner two-replica
graphical representation. Numerical studies of the EA model in
dimension three and rigorous results for the SK model are consistent in
supporting the conclusion that the signature of spin-glass order in these
models is the existence of a single percolating cluster of maximal density
normally coexisting with a second percolating cluster of lower density.Comment: Based on lectures given at the 2007 Paris Summer School "Spin
Glasses." 12 pages, 3 figure
Precambrian non-marine stromatolites in alluvial fan deposits, the Copper Harbor Conglomerate, upper Michigan
Laminated cryptalgal carbonates occur in the Precambrian Copper Harbor Conglomerate of northern Michigan, which was deposited in the Keweenawan Trough, an aborted proto-oceanic rift. This unit is composed of three major facies deposited by braided streams on a large alluvial-fan complex. Coarse clastics were deposited in braided channels, predominantly as longitudinal bars, whereas cross-bedded sandstones were deposited by migrating dunes or linguoid bars. Fine-grained overbank deposits accumulated in abandoned channels. Gypsum moulds and carbonate-filled cracks suggest an arid climate during deposition. Stromatolites interstratified with these clastic facies occur as laterally linked drapes over cobbles, as laterally linked contorted beds in mudstone, as oncolites, and as poorly developed mats in coarse sandstones. Stromatolites also are interbedded with oolitic beds and intraclastic conglomerates. Stromatolitic microstructure consists of alternating detrital and carbonate laminae, and open-space structures. Radial-fibrous calcite fans are superimposed on the laminae. The laminae are interpreted as algal in origin, whereas the origin of the radial fibrous calcite is problematic. The stromatolites are inferred to have grown in lakes which occupied abandoned channels on the fan surface. Standing water on a permeable alluvial fan in an arid climate requires a high water table maintained by high precipitation, or local elevation of the water table, possibly due to the close proximity of a lake. Occurrence of stromatolites in the upper part of the Copper Harbor Conglomerate near the base of the lacustrine Nonesuch Shale suggests that these depositional sites may have been near the Nonesuch Lake.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/72022/1/j.1365-3091.1983.tb00713.x.pd
Massively parallel simulations for disordered systems
Simulations of systems with quenched disorder are extremely demanding,
suffering from the combined effect of slow relaxation and the need of
performing the disorder average. As a consequence, new algorithms, improved
implementations, and alternative and even purpose-built hardware are often
instrumental for conducting meaningful studies of such systems. The ensuing
demands regarding hardware availability and code complexity are substantial and
sometimes prohibitive. We demonstrate how with a moderate coding effort leaving
the overall structure of the simulation code unaltered as compared to a CPU
implementation, very significant speed-ups can be achieved from a parallel code
on GPU by mainly exploiting the trivial parallelism of the disorder samples and
the near-trivial parallelism of the parallel tempering replicas. A combination
of this massively parallel implementation with a careful choice of the
temperature protocol for parallel tempering as well as efficient cluster
updates allows us to equilibrate comparatively large systems with moderate
computational resources.Comment: accepted for publication in EPJB, Topical issue - Recent advances in
the theory of disordered system
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