Conformal field theory correlations in the Abelian sandpile mode

We calculate all multipoint correlation functions of all local bond modifications in the two-dimensional Abelian sandpile model, both at the critical point, and in the model with dissipation. The set of local bond modifications includes, as the most physically interesting case, all weakly allowed cluster variables. The correlation functions show that all local bond modifications have scaling dimension two, and can be written as linear combinations of operators in the central charge -2 logarithmic conformal field theory, in agreement with a form conjectured earlier by Mahieu and Ruelle in Phys. Rev. E 64, 066130 (2001). We find closed form expressions for the coefficients of the operators, and describe methods that allow their rapid calculation. We determine the fields associated with adding or removing bonds, both in the bulk, and along open and closed boundaries; some bond defects have scaling dimension two, while others have scaling dimension four. We also determine the corrections to bulk probabilities for local bond modifications near open and closed boundaries.Comment: 13 pages, 5 figures; referee comments incorporated; Accepted by Phys. Rev.

Dynamic Critical approach to Self-Organized Criticality

A dynamic scaling Ansatz for the approach to the Self-Organized Critical (SOC) regime is proposed and tested by means of extensive simulations applied to the Bak-Sneppen model (BS), which exhibits robust SOC behavior. Considering the short-time scaling behavior of the density of sites ($\rho(t)$) below the critical value, it is shown that i) starting the dynamics with configurations such that $\rho(t=0) \to 0$ one observes an {\it initial increase} of the density with exponent $\theta = 0.12(2)$; ii) using initial configurations with $\rho(t=0) \to 1$, the density decays with exponent $\delta = 0.47(2)$. It is also shown that he temporal autocorrelation decays with exponent $C_a = 0.35(2)$. Using these, dynamically determined, critical exponents and suitable scaling relationships, all known exponents of the BS model can be obtained, e.g. the dynamical exponent $z = 2.10(5)$, the mass dimension exponent $D = 2.42(5)$, and the exponent of all returns of the activity $\tau_{ALL} = 0.39(2)$, in excellent agreement with values already accepted and obtained within the SOC regime.Comment: Rapid Communication Physical Review E in press (4 pages, 5 figures

Unified Scaling Law for Earthquakes

We show that the distribution of waiting times between earthquakes occurring in California obeys a simple unified scaling law valid from tens of seconds to tens of years, see Eq. (1) and Fig. 4. The short time clustering, commonly referred to as aftershocks, is nothing but the short time limit of the general hierarchical properties of earthquakes. There is no unique operational way of distinguishing between main shocks and aftershocks. In the unified law, the Gutenberg-Richter b-value, the exponent -1 of the Omori law for aftershocks, and the fractal dimension d_f of earthquakes appear as critical indices.Comment: 4 pages, 4 figure

The Boltzmann Equation in Scalar Field Theory

We derive the classical transport equation, in scalar field theory with a V(phi) interaction, from the equation of motion for the quantum field. We obtain a very simple, but iterative, expression for the effective action which generates all the n-point Green functions in the high-temperature limit. An explicit closed form is given in the static case.Comment: 10 pages, using RevTeX (corrected TeX misprints

Scale Dependent Dimension of Luminous Matter in the Universe

We present a geometrical model of the distribution of luminous matter in the universe, derived from a very simple reaction-diffusion model of turbulent phenomena. The apparent dimension of luminous matter, $D(l)$, depends linearly on the logarithm of the scale $l$ under which the universe is viewed: $D(l) \sim 3\log(l/l_0)/\log(\xi/l_0)$, where $\xi$ is a correlation length. Comparison with data from the SARS red-shift catalogue, and the LEDA database provides a good fit with a correlation length $\xi \sim 300$ Mpc. The geometrical interpretation is clear: At small distances, the universe is zero-dimensional and point-like. At distances of the order of 1 Mpc the dimension is unity, indicating a filamentary, string-like structure; when viewed at larger scales it gradually becomes 2-dimensional wall-like, and finally, at and beyond the correlation length, it becomes uniform.Comment: 6 pages, 2 figure

A Self-Organized Method for Computing the Epidemic Threshold in Computer Networks

In many cases, tainted information in a computer network can spread in a way similar to an epidemics in the human world. On the other had, information processing paths are often redundant, so a single infection occurrence can be easily "reabsorbed". Randomly checking the information with a central server is equivalent to lowering the infection probability but with a certain cost (for instance processing time), so it is important to quickly evaluate the epidemic threshold for each node. We present a method for getting such information without resorting to repeated simulations. As for human epidemics, the local information about the infection level (risk perception) can be an important factor, and we show that our method can be applied to this case, too. Finally, when the process to be monitored is more complex and includes "disruptive interference", one has to use actual simulations, which however can be carried out "in parallel" for many possible infection probabilities

Complete Supersymmetric Quantum Mechanics of Magnetic Monopoles in N=4 SYM Theory

We find the most general low energy dynamics of 1/2 BPS monopoles in the N=4 supersymmetric Yang-Mills theories (SYM) when all six adjoint Higgs expectation values are turned on. When only one Higgs is turned on, the Lagrangian is purely kinetic. When all six are turned on, however, this moduli space dynamics is augmented by five independent potential terms, each in the form of half the squared norm of a Killing vector field on the moduli space. A generic stationary configuration of the monopoles can be interpreted as stable non BPS dyons, previously found as non-planar string webs connecting D3-branes. The supersymmetric extension is also found explicitly, and gives the complete quantum mechanics of monopoles in N=4 SYM theory. We explore its supersymmetry algebra.Comment: Errors in the SUSY algebra corrected. The version to appear in PR

Generic Criticality in a Model of Evolution

Using Monte Carlo simulations, we show that for a certain model of biological evolution, which is driven by non-extremal dynamics, active and absorbing phases are separated by a critical phase. In this phase both the density of active sites $\rho(t)$ and the survival probability of spreading $P(t)$ decay as $t^{-\delta}$, where $\delta \sim 0.5$. At the critical point, which separates the active and critical phases, $\delta\sim 0.29$, which suggests that this point belongs to the so-called parity-conserving universality class. The model has infinitely many absorbing states and, except for a single point, has no conservation law.Comment: 4 pages, 3 figures, minor grammatical change

Separation of Spontaneous Chiral Symmetry Breaking and Confinement via AdS/CFT Correspondence

We analyze, in the framework of AdS/CFT correspondence, the gauge theory phase structure that are supposed to be dual to the recently found non-supersymmetric dilatonic deformations to AdS_5 X S^5 in type IIB string theory. Analyzing the probe D7-brane dynamics in the backgrounds of our interest, which corresponds to the fundamental N=2 hypermultiplet, we show that the chiral bi-fermion condensation responsible for spontaneous chiral symmetry breaking is not logically related to the phenomenon of confinement.Comment: LaTex, 21 pages, 3 figures. v2: references adde

Flame propagation in random media

We introduce a phase-field model to describe the dynamics of a self-sustaining propagating combustion front within a medium of randomly distributed reactants. Numerical simulations of this model show that a flame front exists for reactant concentration $c > c^* > 0$, while its vanishing at $c^*$ is consistent with mean-field percolation theory. For $c > c^*$, we find that the interface associated with the diffuse combustion zone exhibits kinetic roughening characteristic of the Kardar-Parisi-Zhang equation.Comment: 4, LR541