Related papers: Universal correlations in percolation
The 't Hooft criterion leading to confinement out of a percolating cluster of central vortices suggests defining a novel three-dimensional gauge theory directly on a random percolation process. Wilson loop is viewed as a counter of…
We consider the effects of spatial correlations in a two-dimensional site percolation model. By generalizing the Newman-Ziff Monte Carlo algorithm to include spatial correlations, percolation thresholds and fractal dimensions of percolation…
We study the statistics of a system of N random levels with integer values, in the presence of a logarithmic repulsive potential of Dyson type. This probleme arises in sums over representations (Young tableaux) of GL(N) in various matrix…
Correlators describing the vulcanization transition are constructed and explored via a renormalization group approach. This approach is based on a minimal model that accounts for the thermal motion of constituents and the quenched random…
The generalization of Kasteleyn and Fortuin clusters formalism is introduced in XY (or more generally O(n)) models. Clusters geometrical structure may be linked to spin physical properties as correlation functions. To investigate…
Percolation refers to the emergence of a giant connected cluster in a disordered system when the number of connections between nodes exceeds a critical value. The percolation phase transitions were believed to be continuous until recently…
Spatiotemporal patterns, which are of interest in statistical physics and nonlinear dynamics, form on the tape-peeling trace. Recently, we have proposed a mathematical model to describe these pattern formation in the tape-peeling trace. In…
We study long-range power-law correlated disorder on square and cubic lattices. In particular, we present high-precision results for the percolation thresholds and the fractal dimension of the largest clusters as function of the correlation…
Reply to the comment, cond-mat/0209398 by by N.W. Watkins, S.C. Chapman, and G. Rowlands
The Gaussian model of discontinuous percolation, recently introduced by Ara\'ujo and Herrmann [Phys. Rev. Lett., 105, 035701 (2010)], is numerically investigated in three dimensions, disclosing a discontinuous transition. For the…
The study of percolation in so-called {\em nested subgraphs} implies a generalization of the concept of percolation since the results are not linked to specific graph process. Here the behavior of such graphs at criticallity is studied for…
In the first paper of this series [S. Torquato, J. Chem. Phys. {\bf 136}, 054106 (2012)], analytical results concerning the continuum percolation of overlapping hyperparticles in $d$-dimensional Euclidean space $\mathbb{R}^d$ were obtained,…
We present a unifying, consistent, finite-size-scaling picture for percolation theory bringing it into the framework of a general, renormalization-group-based, scaling scheme for systems above their upper critical dimensions $d_c$.…
Correlations are known to play a crucial role in determining the structure of complex networks. Here we study how their presence affects the computation of the percolation threshold in random hypergraphs. In order to mimic the correlation…
A brief review to string and parton percolation is presented. After a short introduction, the main consequences of percolation of color sources on the following observables in A-A collisions: $J/\psi$ suppression, saturation of the…
We study the Coulomb chain where particles are restricted to one dimension and experience three-dimensional Coulomb interactions with their nearest and next-to-nearest neighbours. The distances between consecutive particles are treated as…
We examine the effects of introducing a wall or edge into a directed percolation process. Scaling ansatzes are presented for the density and survival probability of a cluster in these geometries, and we make the connection to surface…
Percolation, a paradigmatic geometric system in various branches of physical sciences, is known to possess logarithmic factors in its correlators. Starting from its definition, as the $Q\rightarrow1$ limit of the $Q$-state Potts model with…
Percolation theory concerns the emergence of connected clusters that percolate through a networked system. Previous studies ignored the effect that a node outside the percolating cluster may actively induce its inside neighbours to exit the…
We review the basic notion of correlations in point processes, adapted to the language of high energy physicists. The measurement of accessible information on correlations by means of correlation integrals is summarized. Applications to the…