29 research outputs found
Percolation in the Harmonic Crystal and Voter Model in three dimensions
We investigate the site percolation transition in two strongly correlated
systems in three dimensions: the massless harmonic crystal and the voter model.
In the first case we start with a Gibbs measure for the potential,
, , and , a scalar height variable, and define
occupation variables for . The probability
of a site being occupied, is then a function of . In the voter model we
consider the stationary measure, in which each site is either occupied or
empty, with probability . In both cases the truncated pair correlation of
the occupation variables, , decays asymptotically like .
Using some novel Monte Carlo simulation methods and finite size scaling we find
accurate values of as well as the critical exponents for these systems.
The latter are different from that of independent percolation in , as
expected from the work of Weinrib and Halperin [WH] for the percolation
transition of systems with [A. Weinrib and B. Halperin,
Phys. Rev. B 27, 413 (1983)]. In particular the correlation length exponent
is very close to the predicted value of 2 supporting the conjecture by WH
that is exact.Comment: 8 figures. new version significantly different from the old one,
includes new results, figures et
Universality of ac-conduction in anisotropic disordered systems: An effective medium approximation study
Anisotropic disordered system are studied in this work within the random
barrier model. In such systems the transition probabilities in different
directions have different probability density functions. The
frequency-dependent conductivity at low temperatures is obtained using an
effective medium approximation. It is shown that the isotropic universal
ac-conduction law, , is recovered if properly scaled
conductivity () and frequency () variables are used.Comment: 5 pages, no figures, final form (with corrected equations
The time resolution of the St. Petersburg paradox
A resolution of the St. Petersburg paradox is presented. In contrast to the
standard resolution, utility is not required. Instead, the time-average
performance of the lottery is computed. The final result can be phrased
mathematically identically to Daniel Bernoulli's resolution, which uses
logarithmic utility, but is derived using a conceptually different argument.
The advantage of the time resolution is the elimination of arbitrary utility
functions.Comment: 20 pages, 1 figur
Numerical Determination of the Avalanche Exponents of the Bak-Tang-Wiesenfeld Model
We consider the Bak-Tang-Wiesenfeld sandpile model on a two-dimensional
square lattice of lattice sizes up to L=4096. A detailed analysis of the
probability distribution of the size, area, duration and radius of the
avalanches will be given. To increase the accuracy of the determination of the
avalanche exponents we introduce a new method for analyzing the data which
reduces the finite-size effects of the measurements. The exponents of the
avalanche distributions differ slightly from previous measurements and
estimates obtained from a renormalization group approach.Comment: 6 pages, 6 figure
Computer simulation of Wheeler's delayed choice experiment with photons
We present a computer simulation model of Wheeler's delayed choice experiment
that is a one-to-one copy of an experiment reported recently (V. Jacques {\sl
et al.}, Science 315, 966 (2007)). The model is solely based on experimental
facts, satisfies Einstein's criterion of local causality and does not rely on
any concept of quantum theory. Nevertheless, the simulation model reproduces
the averages as obtained from the quantum theoretical description of Wheeler's
delayed choice experiment. Our results prove that it is possible to give a
particle-only description of Wheeler's delayed choice experiment which
reproduces the averages calculated from quantum theory and which does not defy
common sense.Comment: Europhysics Letters (in press
Corpuscular model of two-beam interference and double-slit experiments with single photons
We introduce an event-based corpuscular simulation model that reproduces the
wave mechanical results of single-photon double slit and two-beam interference
experiments and (of a one-to-one copy of an experimental realization) of a
single-photon interference experiment with a Fresnel biprism. The simulation
comprises models that capture the essential features of the apparatuses used in
the experiment, including the single-photon detectors recording individual
detector clicks. We demonstrate that incorporating in the detector model,
simple and minimalistic processes mimicking the memory and threshold behavior
of single-photon detectors is sufficient to produce multipath interference
patterns. These multipath interference patterns are built up by individual
particles taking one single path to the detector where they arrive one-by-one.
The particles in our model are not corpuscular in the standard, classical
physics sense in that they are information carriers that exchange information
with the apparatuses of the experimental set-up. The interference pattern is
the final, collective outcome of the information exchanges of many particles
with these apparatuses. The interference patterns are produced without making
reference to the solution of a wave equation and without introducing signalling
or non-local interactions between the particles or between different detection
points on the detector screen.Comment: Accepted for publication in J. Phys. Soc. Jpn
Fusion algebra of critical percolation
We present an explicit conjecture for the chiral fusion algebra of critical
percolation considering Virasoro representations with no enlarged or extended
symmetry algebra. The representations we take to generate fusion are countably
infinite in number. The ensuing fusion rules are quasi-rational in the sense
that the fusion of a finite number of these representations decomposes into a
finite direct sum of these representations. The fusion rules are commutative,
associative and exhibit an sl(2) structure. They involve representations which
we call Kac representations of which some are reducible yet indecomposable
representations of rank 1. In particular, the identity of the fusion algebra is
a reducible yet indecomposable Kac representation of rank 1. We make detailed
comparisons of our fusion rules with the recent results of Eberle-Flohr and
Read-Saleur. Notably, in agreement with Eberle-Flohr, we find the appearance of
indecomposable representations of rank 3. Our fusion rules are supported by
extensive numerical studies of an integrable lattice model of critical
percolation. Details of our lattice findings and numerical results will be
presented elsewhere.Comment: 12 pages, v2: comments and references adde
W-Extended Fusion Algebra of Critical Percolation
Two-dimensional critical percolation is the member LM(2,3) of the infinite
series of Yang-Baxter integrable logarithmic minimal models LM(p,p'). We
consider the continuum scaling limit of this lattice model as a `rational'
logarithmic conformal field theory with extended W=W_{2,3} symmetry and use a
lattice approach on a strip to study the fundamental fusion rules in this
extended picture. We find that the representation content of the ensuing closed
fusion algebra contains 26 W-indecomposable representations with 8 rank-1
representations, 14 rank-2 representations and 4 rank-3 representations. We
identify these representations with suitable limits of Yang-Baxter integrable
boundary conditions on the lattice and obtain their associated W-extended
characters. The latter decompose as finite non-negative sums of W-irreducible
characters of which 13 are required. Implementation of fusion on the lattice
allows us to read off the fusion rules governing the fusion algebra of the 26
representations and to construct an explicit Cayley table. The closure of these
representations among themselves under fusion is remarkable confirmation of the
proposed extended symmetry.Comment: 30 page