9 research outputs found
Star-graph expansions for bond-diluted Potts models
We derive high-temperature series expansions for the free energy and the
susceptibility of random-bond -state Potts models on hypercubic lattices
using a star-graph expansion technique. This method enables the exact
calculation of quenched disorder averages for arbitrary uncorrelated coupling
distributions. Moreover, we can keep the disorder strength as well as the
dimension as symbolic parameters. By applying several series analysis
techniques to the new series expansions, one can scan large regions of the
parameter space for any value of . For the bond-diluted 4-state
Potts model in three dimensions, which exhibits a rather strong first-order
phase transition in the undiluted case, we present results for the transition
temperature and the effective critical exponent as a function of
as obtained from the analysis of susceptibility series up to order 18. A
comparison with recent Monte Carlo data (Chatelain {\em et al.}, Phys. Rev.
E64, 036120(2001)) shows signals for the softening to a second-order transition
at finite disorder strength.Comment: 8 pages, 6 figure
About the Functional Form of the Parisi Overlap Distribution for the Three-Dimensional Edwards-Anderson Ising Spin Glass
Recently, it has been conjectured that the statistics of extremes is of
relevance for a large class of correlated system. For certain probability
densities this predicts the characteristic large fall-off behavior
, . Using a multicanonical Monte Carlo technique,
we have calculated the Parisi overlap distribution for the
three-dimensional Edward-Anderson Ising spin glass at and below the critical
temperature, even where is exponentially small. We find that a
probability distribution related to extreme order statistics gives an excellent
description of over about 80 orders of magnitude.Comment: 4 pages RevTex, 3 figure
Evidence for softening of first-order transition in 3D by quenched disorder
We study by extensive Monte Carlo simulations the effect of random bond
dilution on the phase transition of the three-dimensional 4-state Potts model
which is known to exhibit a strong first-order transition in the pure case. The
phase diagram in the dilution-temperature plane is determined from the peaks of
the susceptibility for sufficiently large system sizes. In the strongly
disordered regime, numerical evidence for softening to a second-order
transition induced by randomness is given. Here a large-scale finite-size
scaling analysis, made difficult due to strong crossover effects presumably
caused by the percolation fixed point, is performed.Comment: LaTeX file with Revtex, 4 pages, 4 eps figure
Particle Emissions from Domestic Gas Cookers
The authors experimentally studied the formation of submicron particles from a domestic gas cooker in a compartment free from external particle sources. The effects of fuel (methane, natural gas, odorant-free natural gas), primary aeration, flow rate, and fuel sulphur content on particle emissions were investigated. The experiments confirmed reports from literature that blue burning flames of domestic gas cookers emit submicron particles. The particle number concentrations varied in the range 103-106 particles/cm3, depending on the fuel, flow rate, and primary air addition. The diameters of the emitted particles were found to have a mean value of about 7 nm for partially premixed flames, increasing to ∼10 nm for nonpremixed flames. The quantity of primary air had a strong impact on the particle emissions, showing a minimum at a primary aeration level of 60-65%. Presence of sulphur in small quantities may enhance particle formation under some conditions, but results were not conclusive
The Harris-Luck criterion for random lattices
The Harris-Luck criterion judges the relevance of (potentially) spatially
correlated, quenched disorder induced by, e.g., random bonds, randomly diluted
sites or a quasi-periodicity of the lattice, for altering the critical behavior
of a coupled matter system. We investigate the applicability of this type of
criterion to the case of spin variables coupled to random lattices. Their
aptitude to alter critical behavior depends on the degree of spatial
correlations present, which is quantified by a wandering exponent. We consider
the cases of Poissonian random graphs resulting from the Voronoi-Delaunay
construction and of planar, ``fat'' Feynman diagrams and precisely
determine their wandering exponents. The resulting predictions are compared to
various exact and numerical results for the Potts model coupled to these
quenched ensembles of random graphs.Comment: 13 pages, 9 figures, 2 tables, REVTeX 4. Version as published, one
figure added for clarification, minor re-wordings and typo cleanu
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
Scaling and universality in the phase diagram of the 2D Blume-Capel model
We review the pertinent features of the phase diagram of the zero-field
Blume-Capel model, focusing on the aspects of transition order, finite-size
scaling and universality. In particular, we employ a range of Monte Carlo
simulation methods to study the 2D spin-1 Blume-Capel model on the square
lattice to investigate the behavior in the vicinity of the first-order and
second-order regimes of the ferromagnet-paramagnet phase boundary,
respectively. To achieve high-precision results, we utilize a combination of
(i) a parallel version of the multicanonical algorithm and (ii) a hybrid
updating scheme combining Metropolis and generalized Wolff cluster moves. These
techniques are combined to study for the first time the correlation length of
the model, using its scaling in the regime of second-order transitions to
illustrate universality through the observed identity of the limiting value of
with the exactly known result for the Ising universality class.Comment: 16 pages, 7 figures, 1 table, submitted to Eur. Phys. J. Special
Topic
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
General discussion
The Gerhard Herzberg fonds is held at the NRC Archives. Contact [email protected] for information about access.Le fonds Gerhard Herzberg est conserv\ue9 aux Archives du CNRC. Contactez [email protected] pour des informations sur l'acc\ue8s.Peer reviewed: YesNRC publication: Ye