58 research outputs found
On the Aizenman exponent in critical percolation
The probabilities of clusters spanning a hypercube of dimensions two to seven
along one axis of a percolation system under criticality were investigated
numerically. We used a modified Hoshen--Kopelman algorithm combined with
Grassberger's "go with the winner" strategy for the site percolation. We
carried out a finite-size analysis of the data and found that the probabilities
confirm Aizenman's proposal of the multiplicity exponent for dimensions three
to five. A crossover to the mean-field behavior around the upper critical
dimension is also discussed.Comment: 5 pages, 4 figures, 4 table
The RANLUX generator: resonances in a random walk test
Using a recently proposed directed random walk test, we systematically
investigate the popular random number generator RANLUX developed by Luescher
and implemented by James. We confirm the good quality of this generator with
the recommended luxury level. At a smaller luxury level (for instance equal to
1) resonances are observed in the random walk test. We also find that the
lagged Fibonacci and Subtract-with-Carry recipes exhibit similar failures in
the random walk test. A revised analysis of the corresponding dynamical systems
leads to the observation of resonances in the eigenvalues of Jacobi matrix.Comment: 18 pages with 14 figures, Essential addings in the Abstract onl
Periodic orbits of the ensemble of Sinai-Arnold cat maps and pseudorandom number generation
We propose methods for constructing high-quality pseudorandom number
generators (RNGs) based on an ensemble of hyperbolic automorphisms of the unit
two-dimensional torus (Sinai-Arnold map or cat map) while keeping a part of the
information hidden. The single cat map provides the random properties expected
from a good RNG and is hence an appropriate building block for an RNG, although
unnecessary correlations are always present in practice. We show that
introducing hidden variables and introducing rotation in the RNG output,
accompanied with the proper initialization, dramatically suppress these
correlations. We analyze the mechanisms of the single-cat-map correlations
analytically and show how to diminish them. We generalize the Percival-Vivaldi
theory in the case of the ensemble of maps, find the period of the proposed RNG
analytically, and also analyze its properties. We present efficient practical
realizations for the RNGs and check our predictions numerically. We also test
our RNGs using the known stringent batteries of statistical tests and find that
the statistical properties of our best generators are not worse than those of
other best modern generators.Comment: 18 pages, 3 figures, 9 table
Critical properties of joint spin and Fortuin-Kasteleyn observables in the two-dimensional Potts model
The two-dimensional Potts model can be studied either in terms of the
original Q-component spins, or in the geometrical reformulation via
Fortuin-Kasteleyn (FK) clusters. While the FK representation makes sense for
arbitrary real values of Q by construction, it was only shown very recently
that the spin representation can be promoted to the same level of generality.
In this paper we show how to define the Potts model in terms of observables
that simultaneously keep track of the spin and FK degrees of freedom. This is
first done algebraically in terms of a transfer matrix that couples three
different representations of a partition algebra. Using this, one can study
correlation functions involving any given number of propagating spin clusters
with prescribed colours, each of which contains any given number of distinct FK
clusters. For 0 <= Q <= 4 the corresponding critical exponents are all of the
Kac form h_{r,s}, with integer indices r,s that we determine exactly both in
the bulk and in the boundary versions of the problem. In particular, we find
that the set of points where an FK cluster touches the hull of its surrounding
spin cluster has fractal dimension d_{2,1} = 2 - 2 h_{2,1}. If one constrains
this set to points where the neighbouring spin cluster extends to infinity, we
show that the dimension becomes d_{1,3} = 2 - 2 h_{1,3}. Our results are
supported by extensive transfer matrix and Monte Carlo computations.Comment: 15 pages, 3 figures, 2 table
Critical Point Correlation Function for the 2D Random Bond Ising Model
High accuracy Monte Carlo simulation results for 1024*1024 Ising system with
ferromagnetic impurity bonds are presented. Spin-spin correlation function at a
critical point is found to be numerically very close to that of a pure system.
This is not trivial since a critical temperature for the system with impurities
is almost two times lower than pure Ising . Finite corrections to the
correlation function due to combined action of impurities and finite lattice
size are described.Comment: 7 pages, 2 figures after LaTeX fil
KH2PO4 + Host Matrix (Alumina / SiO) Nanocomposite: Raman Scattering Insight
We report on the synthesis and Raman scattering characterization of composite
materials based on the hostnanoporous matrices filled with nanostructured
KH2PO4 (KDP) crystal. Silica (SiO2) and anodized aluminium oxide (AAO) were
used as host matrices with various pore diameters, inter-pore spacing and
morphology. The structure of the nanocomposites was investigated by X-ray
diffraction and scanning electron microscopy. Raman scattering reveals the
creation of one-dimensional nanostructured KDP inside the SiO2 matrix. We
clearly observed the stretching {\nu}1, {\nu}3 and bending {\nu}2 vibrations of
PO4 tetrahedral groups in the Raman spectrum of SiO2 + KDP. In Raman scattering
spectra of AAO + KDP nanocomposite, the broad fluorescence background of AAO
matrix dominates to a great extent, hindering thus the detecting of the KDP
compound spectral response.Comment: 4 pages, 2 figures; 21st International Conference on Transparent
Optical Networks (ICTON) 201
Algorithm for normal random numbers
We propose a simple algorithm for generating normally distributed pseudo
random numbers. The algorithm simulates N molecules that exchange energy among
themselves following a simple stochastic rule. We prove that the system is
ergodic, and that a Maxwell like distribution that may be used as a source of
normally distributed random deviates follows when N tends to infinity. The
algorithm passes various performance tests, including Monte Carlo simulation of
a finite 2D Ising model using Wolff's algorithm. It only requires four simple
lines of computer code, and is approximately ten times faster than the
Box-Muller algorithm.Comment: 5 pages, 3 encapsulated Postscript Figures. Submitted to
Phys.Rev.Letters. For related work, see http://pipe.unizar.es/~jf
Quenched bond dilution in two-dimensional Potts models
We report a numerical study of the bond-diluted 2-dimensional Potts model
using transfer matrix calculations. For different numbers of states per spin,
we show that the critical exponents at the random fixed point are the same as
in self-dual random-bond cases. In addition, we determine the multifractal
spectrum associated with the scaling dimensions of the moments of the spin-spin
correlation function in the cylinder geometry. We show that the behaviour is
fully compatible with the one observed in the random bond case, confirming the
general picture according to which a unique fixed point describes the critical
properties of different classes of disorder: dilution, self-dual binary
random-bond, self-dual continuous random bond.Comment: LaTeX file with IOP macros, 29 pages, 14 eps figure
Critical domain walls in the Ashkin-Teller model
We study the fractal properties of interfaces in the 2d Ashkin-Teller model.
The fractal dimension of the symmetric interfaces is calculated along the
critical line of the model in the interval between the Ising and the
four-states Potts models. Using Schramm's formula for crossing probabilities we
show that such interfaces can not be related to the simple SLE, except
for the Ising point. The same calculation on non-symmetric interfaces is
performed at the four-states Potts model: the fractal dimension is compatible
with the result coming from Schramm's formula, and we expect a simple
SLE in this case.Comment: Final version published in JSTAT. 13 pages, 5 figures. Substantial
changes in the data production, analysis and in the conclusions. Added a
section about the crossing probability. Typeset with 'iopart
A new test for random number generators: Schwinger-Dyson equations for the Ising model
We use a set of Schwinger-Dyson equations for the Ising Model to check
several random number generators. For the model in two and three dimensions, it
is shown that the equations are sensitive tests of bias originated by the
random numbers. The method is almost costless in computer time when added to
any simulation.Comment: 6 pages, 3 figure
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