Related papers: Finite size scaling study of a two parameter perco…
The percolation threshold for flow or conduction through voids surrounding randomly placed spheres is rigorously calculated. With large scale Monte Carlo simulations, we give a rigorous continuum treatment to the geometry of the…
Criticality is traditionally regarded as an unstable, fine-tuned fixed point of the renormalization group. We introduce an iterative bicolored percolation process in two dimensions and show that it can both preserve criticality and…
Recently, a simple non-interacting-electron model, combining local quantum tunneling via quantum point contacts and global classical percolation, has been introduced in order to describe the observed ``metal-insulator transition'' in two…
We present structural properties of two-dimensional polymers as far as they can be described by percolation theory. The percolation threshold, critical exponents and fractal dimensions of clusters are determined by computer simulation and…
We report on the exact treatment of a random-matrix representation of bond percolation model on a square lattice in two dimensions with occupation probability $p$. The percolation problem is mapped onto a random complex matrix composed of…
We present the results of a percolation-like model that has been restricted compared to standard percolation models in the sense that we do not allow finite sized clusters to break up once they have formed. We calculate the critical…
For ordinary (independent) percolation on a large class of lattices it is well known that below the critical percolation parameter $p_c$ the cluster size distribution has exponential decay and that power-law behavior of this distribution…
Linear rate equations are used to describe the cascading decay of an initial heavy cluster into fragments. We consider moments of arbitrary orders of the mass multiplicity spectrum and derive scaling properties pertaining to their time…
We discuss the universal scaling laws of order parameter fluctuations in any system in which the second-order critical behaviour can be identified. These scaling laws can be derived rigorously for equilibrium systems when combined with the…
Two-dimensional directed site percolation is studied in systems directed along the x-axis and limited by a free surface at y=\pm Cx^k. Scaling considerations show that the surface is a relevant perturbation to the local critical behaviour…
We study the scaling of the average cluster size and percolation strength of geometrical clusters for the two-dimensional Ising model. By means of Monte Carlo simulations and a finite-size scaling analysis we discuss the appearance of…
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 $L$…
The critical phase of bond percolation on the random growing tree is examined. It is shown that the root cluster grows with the system size $N$ as $N^\psi$ and the mean number of clusters with size $s$ per node follows a power function $n_s…
We present large scale simulations of a stochastic sandpile model in two dimensions. We use moments analysis to evaluate critical exponents and finite size scaling method to consistently test the obtained results. The general picture…
Binary mixtures prepared in an homogeneous phase and quenched into a two-phase region phase-separate via a coarsening process whereby domains of the two phases grow in time. With a numerical study of a spin-exchange model we show that this…
Transient dynamics leading to the synchrony of pulse-coupled oscillators has previously been studied as an aggregation process of synchronous clusters, and a rate equation for the cluster size distribution has been proposed. However, the…
In this letter, we focus on the size effect of granular column collapses, which are potentially connected to the dynamics of complex geophysical flows, even if the link between microscopic structures of granular assemblies and their…
The talk presented at ICMP 97 focused on the scaling limits of critical percolation models, and some other systems whose salient features can be described by collections of random lines. In the scaling limit we keep track of features seen…
We present a new unified theory of critical finite-size scaling for lattice statistical mechanical models with periodic boundary conditions above the upper critical dimension. Our theory is based on recent mathematically rigorous results…
For systems with infinite-order phase transitions, in which an order parameter smoothly becomes nonzero, a new observable for finite-size scaling analysis is suggested. By construction this new observable has the favourable property of…