Related papers: Crossover from Isotropic to Directed Percolation
Scaling theory, duality symmetry, and numerical simulations of a random network model are used to study the magnetoresistance of a metal/insulator/perfect conductor composite with a disordered columnar microstructure. The phase diagram is…
The random-cluster model is a dependent percolation model that has applications in the study of Ising and Potts models. In this paper, several new results are obtained for the random-cluster model on nonamenable graphs with cluster…
The structure of many real networks is not locally tree-like and hence, network analysis fails to characterise their bond percolation properties. In a recent paper [P. Mann, V. A. Smith, J. B. O. Mitchell, and S. Dobson, Percolation in…
We study existence of percolation in the hierarchical group of order $N$, which is an ultrametric space, and transience and recurrence of random walks on the percolation clusters. The connection probability on the hierarchical group for two…
The eigenvalue spectra of the transition probability matrix for random walks traversing critically disordered clusters in three different types of percolation problems show that the random walker sees a developing Euclidean signature for…
This paper presents a Monte-Carlo study of percolation in a distorted square lattice, in which, the adjacent sites are not equidistant. Starting with an undistorted lattice, the position of the lattice sites are shifted through a tunable…
Diffusion-limited aggregation is consistent with simple scaling. However, strong subdominant terms are present, and these can account for various earlier claims of anomalous scaling. We show this in detail for the case of multiscaling.
We study models of correlated percolation where there are constraints on the occupation of sites that mimic force-balance, i.e. for a site to be stable requires occupied neighboring sites in all four compass directions in two dimensions. We…
Crossover behaviors from the pair contact process with diffusion (PCPD) and the driven PCPD (DPCPD) to the directed percolation (DP) are studied in one dimension by introducing a single particle annihilation/branching dynamics. The…
Scaling theory predicts complete localization in $d=2$ in quantum systems belonging to orthogonal class (i.e. with time-reversal symmetry and spin-rotation symmetry). The conductance $g$ behaves as $g \sim exp(-L/l)$ with system size $L$…
In this article, we consider an anisotropic finite-range bond percolation model on $\mathbb{Z}^2$. On each horizontal layer $\{(x,i): x \in \mathbb{Z}\}$ we have edges $\langle(x, i),(y, i)\rangle$ for $1 \leq |x - y| \leq N$. There are…
The aim of the paper is to present numerical results supporting the presence of conformal invariance in three dimensional statistical mechanics models at criticality and to elucidate the geometric aspects of universality. As a case study we…
We study the crossover scaling behavior of the height-height correlation function in interface depinning in random media. We analyze experimental data from a fracture experiment and simulate an elastic line model with non-linear couplings…
Scanning probes reveal complex, inhomogeneous patterns on the surface of many condensed matter systems. In some cases, the patterns form self-similar, fractal geometric clusters. In this paper, we advance the theory of criticality as it…
We study resistor diode percolation at the transition from the non-percolating to the directed percolating phase. We derive a field theoretic Hamiltonian which describes not only geometric aspects of directed percolation clusters but also…
Studies of disordered heterogeneous media and galaxy cosmology share a common goal: analyzing the distribution of particles at `microscales' to predict physical properties at `macroscales', whether for a liquid, composite material, or…
For Encyclopedia of Complexity and Systems Science (Springer Verlag). No abstract. I. Definition and Introduction II. Methods III. Quantities and Exponents IV. Fractal Dimension; Incipient Infinite Cluster V. Simple Renormalisation Group…
Phenomenological scaling arguments suggest the existence of universal amplitudes in the finite-size scaling of certain correlation lengths in strongly anisotropic or dynamical phase transitions. For equilibrium systems, provided that…
A two parameter percolation model with nucleation and growth of finite clusters is developed taking the initial seed concentration \rho and a growth parameter g as two tunable parameters. Percolation transition is determined by the final…
We show by means of continuum theory and simulations that geometric percolation in uniaxial nematics of hard slender particles is fundamentally different from that in isotropic dispersions. In the nematic, percolation depends only very…