295 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
Bianchi type II,III and V diagonal Einstein metrics re-visited
We present, for both minkowskian and euclidean signatures, short derivations
of the diagonal Einstein metrics for Bianchi type II, III and V. For the first
two cases we show the integrability of the geodesic flow while for the third
case a somewhat unusual bifurcation phenomenon takes place: for minkowskian
signature elliptic functions are essential in the metric while for euclidean
signature only elementary functions appear
Beyond Blobs in Percolation Cluster Structure: The Distribution of 3-Blocks at the Percolation Threshold
The incipient infinite cluster appearing at the bond percolation threshold
can be decomposed into singly-connected ``links'' and multiply-connected
``blobs.'' Here we decompose blobs into objects known in graph theory as
3-blocks. A 3-block is a graph that cannot be separated into disconnected
subgraphs by cutting the graph at 2 or fewer vertices. Clusters, blobs, and
3-blocks are special cases of -blocks with , 2, and 3, respectively. We
study bond percolation clusters at the percolation threshold on 2-dimensional
square lattices and 3-dimensional cubic lattices and, using Monte-Carlo
simulations, determine the distribution of the sizes of the 3-blocks into which
the blobs are decomposed. We find that the 3-blocks have fractal dimension
in 2D and in 3D. These fractal dimensions are
significantly smaller than the fractal dimensions of the blobs, making possible
more efficient calculation of percolation properties. Additionally, the
closeness of the estimated values for in 2D and 3D is consistent with the
possibility that is dimension independent. Generalizing the concept of
the backbone, we introduce the concept of a ``-bone'', which is the set of
all points in a percolation system connected to disjoint terminal points
(or sets of disjoint terminal points) by disjoint paths. We argue that the
fractal dimension of a -bone is equal to the fractal dimension of
-blocks, allowing us to discuss the relation between the fractal dimension
of -blocks and recent work on path crossing probabilities.Comment: All but first 2 figs. are low resolution and are best viewed when
printe
Further results on non-diagonal Bianchi type III vacuum metrics
We present the derivation, for these vacuum metrics, of the Painlev\'e VI
equation first obtained by Christodoulakis and Terzis, from the field equations
for both minkowskian and euclidean signatures. This allows a complete
discussion and the precise connection with some old results due to Kinnersley.
The hyperk\"ahler metrics are shown to belong to the Multi-Centre class and for
the cases exhibiting an integrable geodesic flow the relevant Killing tensors
are given. We conclude by the proof that for the Bianchi B family, excluding
type III, there are no hyperk\"ahler metrics.Comment: 21 pages, no figure
On the estimation of the curvatures and bending rigidity of membrane networks via a local maximum-entropy approach
We present a meshfree method for the curvature estimation of membrane
networks based on the Local Maximum Entropy approach recently presented in
(Arroyo and Ortiz, 2006). A continuum regularization of the network is carried
out by balancing the maximization of the information entropy corresponding to
the nodal data, with the minimization of the total width of the shape
functions. The accuracy and convergence properties of the given curvature
prediction procedure are assessed through numerical applications to benchmark
problems, which include coarse grained molecular dynamics simulations of the
fluctuations of red blood cell membranes (Marcelli et al., 2005; Hale et al.,
2009). We also provide an energetic discrete-to-continuum approach to the
prediction of the zero-temperature bending rigidity of membrane networks, which
is based on the integration of the local curvature estimates. The Local Maximum
Entropy approach is easily applicable to the continuum regularization of
fluctuating membranes, and the prediction of membrane and bending elasticities
of molecular dynamics models
Percolation on two- and three-dimensional lattices
In this work we apply a highly efficient Monte Carlo algorithm recently
proposed by Newman and Ziff to treat percolation problems. The site and bond
percolation are studied on a number of lattices in two and three dimensions.
Quite good results for the wrapping probabilities, correlation length critical
exponent and critical concentration are obtained for the square, simple cubic,
HCP and hexagonal lattices by using relatively small systems. We also confirm
the universal aspect of the wrapping probabilities regarding site and bond
dilution.Comment: 15 pages, 6 figures, 3 table
Percolation in three-dimensional random field Ising magnets
The structure of the three-dimensional random field Ising magnet is studied
by ground state calculations. We investigate the percolation of the minority
spin orientation in the paramagnetic phase above the bulk phase transition,
located at [Delta/J]_c ~= 2.27, where Delta is the standard deviation of the
Gaussian random fields (J=1). With an external field H there is a disorder
strength dependent critical field +/- H_c(Delta) for the down (or up) spin
spanning. The percolation transition is in the standard percolation
universality class. H_c ~ (Delta - Delta_p)^{delta}, where Delta_p = 2.43 +/-
0.01 and delta = 1.31 +/- 0.03, implying a critical line for Delta_c < Delta <=
Delta_p. When, with zero external field, Delta is decreased from a large value
there is a transition from the simultaneous up and down spin spanning, with
probability Pi_{uparrow downarrow} = 1.00 to Pi_{uparrow downarrow} = 0. This
is located at Delta = 2.32 +/- 0.01, i.e., above Delta_c. The spanning cluster
has the fractal dimension of standard percolation D_f = 2.53 at H = H_c(Delta).
We provide evidence that this is asymptotically true even at H=0 for Delta_c <
Delta <= Delta_p beyond a crossover scale that diverges as Delta_c is
approached from above. Percolation implies extra finite size effects in the
ground states of the 3D RFIM.Comment: replaced with version to appear in Physical Review
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
Infrared exponents and the strong-coupling limit in lattice Landau gauge
We study the gluon and ghost propagators of lattice Landau gauge in the
strong-coupling limit beta=0 in pure SU(2) lattice gauge theory to find
evidence of the conformal infrared behavior of these propagators as predicted
by a variety of functional continuum methods for asymptotically small momenta
. In the strong-coupling limit, this same
behavior is obtained for the larger values of a^2q^2 (in units of the lattice
spacing a), where it is otherwise swamped by the gauge field dynamics.
Deviations for a^2q^2 < 1 are well parameterized by a transverse gluon mass
. Perhaps unexpectedly, these deviations are thus no finite-volume
effect but persist in the infinite-volume limit. They furthermore depend on the
definition of gauge fields on the lattice, while the asymptotic conformal
behavior does not. We also comment on a misinterpretation of our results by
Cucchieri and Mendes in Phys. Rev. D81 (2010) 016005.Comment: 17 pages, 12 figures. Revised version (mainly sections I and II);
references and comments on subsequent work on the subject added
Segregated tunneling-percolation model for transport nonuniversality
We propose a theory of the origin of transport nonuniversality in disordered
insulating-conducting compounds based on the interplay between microstructure
and tunneling processes between metallic grains dispersed in the insulating
host. We show that if the metallic phase is arranged in quasi-one dimensional
chains of conducting grains, then the distribution function of the chain
conductivities g has a power-law divergence for g -> 0 leading to nonuniversal
values of the transport critical exponent t. We evaluate the critical exponent
t by Monte Carlo calculations on a cubic lattice and show that our model can
describe universal as well nonuniversal behavior of transport depending on the
value of few microstructural parameters. Such segregated tunneling-percolation
model can describe the microstructure of a quite vast class of materials known
as thick-film resistors which display universal or nonuniversal values of t
depending on the composition.Comment: 8 pages, 5 figures (Phys. Rev. B - 1 August 2003)(fig1 replaced
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