4,103 research outputs found
Cluster simulations of loop models on two-dimensional lattices
We develop cluster algorithms for a broad class of loop models on
two-dimensional lattices, including several standard O(n) loop models at n \ge
1. We show that our algorithm has little or no critical slowing-down when 1 \le
n \le 2. We use this algorithm to investigate the honeycomb-lattice O(n) loop
model, for which we determine several new critical exponents, and a
square-lattice O(n) loop model, for which we obtain new information on the
phase diagram.Comment: LaTex2e, 4 pages; includes 1 table and 2 figures. Totally rewritten
in version 2, with new theory and new data. Version 3 as published in PR
Grassmann Integral Representation for Spanning Hyperforests
Given a hypergraph G, we introduce a Grassmann algebra over the vertex set,
and show that a class of Grassmann integrals permits an expansion in terms of
spanning hyperforests. Special cases provide the generating functions for
rooted and unrooted spanning (hyper)forests and spanning (hyper)trees. All
these results are generalizations of Kirchhoff's matrix-tree theorem.
Furthermore, we show that the class of integrals describing unrooted spanning
(hyper)forests is induced by a theory with an underlying OSP(1|2)
supersymmetry.Comment: 50 pages, it uses some latex macros. Accepted for publication on J.
Phys.
Critical speeding-up in a local dynamics for the random-cluster model
We study the dynamic critical behavior of the local bond-update (Sweeny)
dynamics for the Fortuin-Kasteleyn random-cluster model in dimensions d=2,3, by
Monte Carlo simulation. We show that, for a suitable range of q values, the
global observable S_2 exhibits "critical speeding-up": it decorrelates well on
time scales much less than one sweep, so that the integrated autocorrelation
time tends to zero as the critical point is approached. We also show that the
dynamic critical exponent z_{exp} is very close (possibly equal) to the
rigorous lower bound \alpha/\nu, and quite possibly smaller than the
corresponding exponent for the Chayes-Machta-Swendsen-Wang cluster dynamics.Comment: LaTex2e/revtex4, 4 pages, includes 5 figure
Corrections to scaling in multicomponent polymer solutions
We calculate the correction-to-scaling exponent that characterizes
the approach to the scaling limit in multicomponent polymer solutions. A direct
Monte Carlo determination of in a system of interacting
self-avoiding walks gives . A field-theory analysis based
on five- and six-loop perturbative series leads to . We
also verify the renormalization-group predictions for the scaling behavior
close to the ideal-mixing point.Comment: 21 page
Consistent coarse-graining strategy for polymer solutions in the thermal crossover from Good to Theta solvent
We extend our previously developed coarse-graining strategy for linear
polymers with a tunable number n of effective atoms (blobs) per chain [D'Adamo
et al., J. Chem. Phys. 137, 4901 (2012)] to polymer systems in thermal
crossover between the good-solvent and the Theta regimes. We consider the
thermal crossover in the region in which tricritical effects can be neglected,
i.e. not too close to the Theta point, for a wide range of chain volume
fractions Phi=c/c* (c* is the overlap concentration), up to Phi=30. Scaling
crossover functions for global properties of the solution are obtained by
Monte-Carlo simulations of the Domb-Joyce model. They provide the input data to
develop a minimal coarse-grained model with four blobs per chain. As in the
good-solvent case, the coarse-grained model potentials are derived at zero
density, thus avoiding the inconsistencies related to the use of
state-dependent potentials. We find that the coarse-grained model reproduces
the properties of the underlying system up to some reduced density which
increases when lowering the temperature towards the Theta state. Close to the
lower-temperature crossover boundary, the tetramer model is accurate at least
up to Phi<10, while near the good-solvent regime reasonably accurate results
are obtained up to Phi<2. The density region in which the coarse-grained model
is predictive can be enlarged by developing coarse-grained models with more
blobs per chain. We extend the strategy used in the good-solvent case to the
crossover regime. This requires a proper treatment of the length rescalings as
before, but also a proper temperature redefinition as the number of blobs is
increased. The case n=10 is investigated. Comparison with full-monomer results
shows that the density region in which accurate predictions can be obtained is
significantly wider than that corresponding to the n=4 case.Comment: 21 pages, 14 figure
Epidemiological patterns of hepatitis B virus (HBV) in highly endemic areas
This paper uses meta-analysis of published data and a deterministic mathematical model of hepatitis B virus (HBV) transmission to describe the patterns of HBV infection in high endemicity areas. We describe the association between the prevalence of carriers and a simple measure of the rate of infection, the age at which half the population have been infected (A50), and assess the contribution of horizontal and perinatal transmission to this association. We found that the two main hyper-endemic areas of sub-Saharan Africa and east Asia have similar prevalences of carriers and values of A50, and that there is a negative nonlinear relationship between A50 and the prevalence of carriers in high endemicity areas (Spearman's Rank, P = 0·0086). We quantified the risk of perinatal transmission and the age-dependent rate of infection to allow a comparison between the main hyper-endemic areas. East Asia was found to have higher prevalences of HBeAg positive mothers and a greater risk of perinatal transmission from HBeAg positive mothers than sub-Saharan Africa, though the differences were not statistically significant. However, the two areas have similar magnitudes and age-dependent rates of horizontal transmission. Results of a simple compartmental model suggest that similar rates of horizontal transmission are sufficient to generate the similar patterns between A50 and the prevalences of carriers. Interrupting horizontal transmission by mass immunization is expected to have a significant, nonlinear impact on the rate of acquisition of new carriers
Dynamic Critical Behavior of the Swendsen-Wang Algorithm: The Two-Dimensional 3-State Potts Model Revisited
We have performed a high-precision Monte Carlo study of the dynamic critical
behavior of the Swendsen-Wang algorithm for the two-dimensional 3-state Potts
model. We find that the Li-Sokal bound ()
is almost but not quite sharp. The ratio seems to diverge
either as a small power () or as a logarithm.Comment: 35 pages including 3 figures. Self-unpacking file containing the
LaTeX file, the needed macros (epsf.sty, indent.sty, subeqnarray.sty, and
eqsection.sty) and the 3 Postscript figures. Revised version fixes a
normalization error in \xi (with many thanks to Wolfhard Janke for finding
the error!). To be published in J. Stat. Phys. 87, no. 1/2 (April 1997
Hot and repulsive traffic flow
We study a message passing model, applicable also to traffic problems. The
model is implemented in a discrete lattice, where particles move towards their
destination, with fluctuations around the minimal distance path. A repulsive
interaction between particles is introduced in order to avoid the appearance of
traffic jam. We have studied the parameter space finding regions of fluid
traffic, and saturated ones, being separated by abrupt changes. The improvement
of the system performance is also explored, by the introduction of a
non-constant potential acting on the particles. Finally, we deal with the
behavior of the system when temporary failures in the transmission occurs.Comment: 22 pages, uuencoded gzipped postscript file. 11 figures include
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
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