Corrections to Universal Fluctuations in Correlated Systems: the 2D XY-model

Generalized universality, as recently proposed, postulates a universal non-Gaussian form of the probability density function (PDF) of certain global observables for a wide class of highly correlated systems of finite volume N. Studying the 2D XY -model, we link its validity to renormalization group properties. It would be valid if there were a single dimension 0 operator, but the actual existence of several such operators leads to T-dependent corrections. The PDF is the Fourier transform of the partition function Z(q) of an auxiliary theory which differs by a dimension 0 perturbation with a very small imaginary coefficient iq/N from a theory which is asymptotically free in the infrared. We compute the PDF from a systematic loop expansion of ln Z(q).Comment: To be published in Phys. Rev.

Different hierarchy of avalanches observed in the Bak-Sneppen evolution model

We introduce a new quantity, average fitness, into the Bak-Sneppen evolution model. Through the new quantity, a different hierarchy of avalanches is observed. The gap equation, in terms of the average fitness, is presented to describe the self-organization of the model. It is found that the critical value of the average fitness can be exactly obtained. Based on the simulations, two critical exponents, avalanche distribution and avalanche dimension, of the new avalanches are given.Comment: 5 pages, 3 figure

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

Crossover from Percolation to Self-Organized Criticality

We include immunity against fire as a new parameter into the self-organized critical forest-fire model. When the immunity assumes a critical value, clusters of burnt trees are identical to percolation clusters of random bond percolation. As long as the immunity is below its critical value, the asymptotic critical exponents are those of the original self-organized critical model, i.e. the system performs a crossover from percolation to self-organized criticality. We present a scaling theory and computer simulation results.Comment: 4 pages Revtex, two figures included, to be published in PR

The origin of power-law distributions in self-organized criticality

The origin of power-law distributions in self-organized criticality is investigated by treating the variation of the number of active sites in the system as a stochastic process. An avalanche is then regarded as a first-return random walk process in a one-dimensional lattice. Power law distributions of the lifetime and spatial size are found when the random walk is unbiased with equal probability to move in opposite directions. This shows that power-law distributions in self-organized criticality may be caused by the balance of competitive interactions. At the mean time, the mean spatial size for avalanches with the same lifetime is found to increase in a power law with the lifetime.Comment: 4 pages in RevTeX, 3 eps figures. To appear in J.Phys.G. To appear in J. Phys.

Renormalization group approach to the critical behavior of the forest fire model

We introduce a Renormalization scheme for the one and two dimensional Forest-Fire models in order to characterize the nature of the critical state and its scale invariant dynamics. We show the existence of a relevant scaling field associated with a repulsive fixed point. This model is therefore critical in the usual sense because the control parameter has to be tuned to its critical value in order to get criticality. It turns out that this is not just the condition for a time scale separation. The critical exponents are computed analytically and we obtain $\nu=1.0$, $\tau=1.0$ and $\nu=0.65$, $\tau=1.16$ respectively for the one and two dimensional case, in very good agreement with numerical simulations.Comment: 4 pages, 3 uuencoded Postcript figure

Avalanche Merging and Continuous Flow in a Sandpile Model

A dynamical transition separating intermittent and continuous flow is observed in a sandpile model, with scaling functions relating the transport behaviors between both regimes. The width of the active zone diverges with system size in the avalanche regime but becomes very narrow for continuous flow. The change of the mean slope, Delta z, on increasing the driving rate, r, obeys Delta z ~ r^{1/theta}. It has nontrivial scaling behavior in the continuous flow phase with an exponent theta given, paradoxically, only in terms of exponents characterizing the avalanches theta = (1+z-D)/(3-D).Comment: Explanations added; relation to other model

Scaling laws and simulation results for the self--organized critical forest--fire model

We discuss the properties of a self--organized critical forest--fire model which has been introduced recently. We derive scaling laws and define critical exponents. The values of these critical exponents are determined by computer simulations in 1 to 8 dimensions. The simulations suggest a critical dimension $d_c=6$ above which the critical exponents assume their mean--field values. Changing the lattice symmetry and allowing trees to be immune against fire, we show that the critical exponents are universal.Comment: 12 pages, postscript uuencoded, figures included, to appear in Phys. Rev.

Correlations and invariance of seismicity under renormalization-group transformations

The effect of transformations analogous to those of the real-space renormalization group are analyzed for the temporal occurrence of earthquakes. The distribution of recurrence times turns out to be invariant under such transformations, for which the role of the correlations between the magnitudes and the recurrence times are fundamental. A general form for the distribution is derived imposing only the self-similarity of the process, which also yields a scaling relation between the Gutenberg-Richter b-value, the exponent characterizing the correlations, and the recurrence-time exponent. This approach puts the study of the structure of seismicity in the context of critical phenomena.Comment: Short paper. I'll be grateful to get some feedbac

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