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 $k$ increases. The model also shows that given the coupling effect among bystanders, for a certain range of small $k$ the helping rate increases according to $k$ 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 $\lambda \phi^4$ field theories describe many critical phenomena in the laboratory and in the early Universe. Given N and $D\leq 3$, 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 $p_2$=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