145 research outputs found
On Damage Spreading Transitions
We study the damage spreading transition in a generic one-dimensional
stochastic cellular automata with two inputs (Domany-Kinzel model) Using an
original formalism for the description of the microscopic dynamics of the
model, we are able to show analitically that the evolution of the damage
between two systems driven by the same noise has the same structure of a
directed percolation problem. By means of a mean field approximation, we map
the density phase transition into the damage phase transition, obtaining a
reliable phase diagram. We extend this analysis to all symmetric cellular
automata with two inputs, including the Ising model with heath-bath dynamics.Comment: 12 pages LaTeX, 2 PostScript figures, tar+gzip+u
Rescue Model for the Bystanders' Intervention in Emergencies
To investigate an effect of social interaction on the bystanders'
intervention in emergency situations we introduce a rescue model which includes
the effects of the victim's acquaintance with bystanders and those among
bystanders. This model reproduces the surprising experimental result that the
helping rate tends to decrease although the number of bystanders increases.
The model also shows that given the coupling effect among bystanders, for a
certain range of small the helping rate increases according to and that
coupling effect plays both positive and negative roles in emergencies. Finally
we find a broad range of coupling strength to maximize the helping rate.Comment: 10 pages, 4 figure
Finite Size Effects in Separable Recurrent Neural Networks
We perform a systematic analytical study of finite size effects in separable
recurrent neural network models with sequential dynamics, away from saturation.
We find two types of finite size effects: thermal fluctuations, and
disorder-induced `frozen' corrections to the mean-field laws. The finite size
effects are described by equations that correspond to a time-dependent
Ornstein-Uhlenbeck process. We show how the theory can be used to understand
and quantify various finite size phenomena in recurrent neural networks, with
and without detailed balance.Comment: 24 pages LaTex, with 4 postscript figures include
Predicting the critical density of topological defects in O(N) scalar field theories
O(N) symmetric field theories describe many critical
phenomena in the laboratory and in the early Universe. Given N and ,
the dimension of space, these models exhibit topological defect classical
solutions that in some cases fully determine their critical behavior. For N=2,
D=3 it has been observed that the defect density is seemingly a universal
quantity at T_c. We prove this conjecture and show how to predict its value
based on the universal critical exponents of the field theory. Analogously, for
general N and D we predict the universal critical densities of domain walls and
monopoles, for which no detailed thermodynamic study exists. This procedure can
also be inverted, producing an algorithm for generating typical defect networks
at criticality, in contrast to the canonical procedure, which applies only in
the unphysical limit of infinite temperature.Comment: 4 pages, 3 figures, uses RevTex, typos in Eq.(11) and (14) correcte
Reentrant Behavior in the Domany-Kinzel Cellular Automaton
We present numerical and analytical results for a special kind of
one-dimensional probabilistic cellular automaton, the so called Domany-Kinzel
automaton. It is shown that the phase boundary separating the active and the
recently found chaotic phase exhibits reentrant behavior. Furthermore exact
results for the =0-line are discussed.Comment: LaTeX 9 pages + 6 figures (appended as uuencoded compressed
tar-file), THP31-9
Vortex Loop Phase Transitions in Liquid Helium, Cosmic Strings, and High-T_c Superconductors
The distribution of thermally excited vortex loops near a superfluid phase
transition is calculated from a renormalized theory. The number density of
loops with a given perimeter is found to change from exponential decay with
increasing perimeter to algebraic decay as T_c is approached, in agreement with
recent simulations of both cosmic strings and high-T_c superconductors.
Predictions of the value of the exponent of the algebraic decay at T_c and of
critical behavior in the vortex density are confirmed by the simulations,
giving strong support to the vortex-folding model proposed by Shenoy.Comment: Version to appear in Phys. Rev. Lett, with a number of corrections
and addition
A vortex description of the first-order phase transition in type-I superconductors
Using both analytical arguments and detailed numerical evidence we show that
the first order transition in the type-I 2D Abelian Higgs model can be
understood in terms of the statistical mechanics of vortices, which behave in
this regime as an ensemble of attractive particles. The well-known
instabilities of such ensembles are shown to be connected to the process of
phase nucleation. By characterizing the equation of state for the vortex
ensemble we show that the temperature for the onset of a clustering instability
is in qualitative agreement with the critical temperature. Below this point the
vortex ensemble collapses to a single cluster, which is a non-extensive phase,
and disappears in the absence of net topological charge. The vortex description
provides a detailed mechanism for the first order transition, which applies at
arbitrarily weak type-I and is gauge invariant unlike the usual field-theoretic
considerations, which rely on asymptotically large gauge coupling.Comment: 4 pages, 6 figures, uses RevTex. Additional references added, some
small corrections to the tex
Vortex-line liquid phases: Longitudinal superconductivity in the lattice London model
We study the vortex-line lattice and liquid phases of a clean type-II
superconductor by means of Monte Carlo simulations of the lattice London model.
Motivated by a recent controversy regarding the presence, within this model, of
a vortex-liquid regime with longitudinal superconducting coherence over long
length scales, we directly compare two different ways to calculate the
longitudinal coherence. For an isotropic superconductor, we interpret our
results in terms of a temperature regime within the liquid phase in which
longitudinal superconducting coherence extends over length scales larger than
the system thickness studied. We note that this regime disappears in the
moderately anisotropic case due to a proliferation, close to the flux-line
lattice melting temperature, of vortex loops between the layers.Comment: 8 pages, Revtex, with eps figures. To appear in Phys. Rev.
The Ginzburg regime and its effects on topological defect formation
The Ginzburg temperature has historically been proposed as the energy scale
of formation of topological defects at a second order symmetry breaking phase
transition. More recently alternative proposals which compute the time of
formation of defects from the critical dynamics of the system, have been
gaining both theoretical and experimental support. We investigate, using a
canonical model for string formation, how these two pictures compare. In
particular we show that prolonged exposure of a critical field configuration to
the Ginzburg regime results in no substantial suppression of the final density
of defects formed. These results dismiss the recently proposed role of the
Ginzburg regime in explaining the absence of topological defects in 4He
pressure quench experiments.Comment: 8 pages, 5 ps figure
Fluctuating diamagnetism in underdoped high temperature superconductors
The fluctuation induced diamagnetism of underdoped high temperature
superconductors is studied in the framework of the Lawrence-Doniach model. By
taking into account the fluctuations of the phase of the order parameter only,
the latter reduces to a layered XY-model describing a liquid of vortices which
can be either thermally excited or induced by the external magnetic field. The
diamagnetic response is given by a current-current correlation function which
is evaluated using the Coulomb gas analogy. Our results are then applied to
recent measurements of fluctuation diamagnetism in underdoped YBCO. They allow
to understand both the observed anomalous temperature dependence of the
zero-field susceptibility and the two distinct regimes appearing in the
magnetic field dependence of the magnetization.Comment: 12 pages, 4 figures included, accepted for publication in PR
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