Related papers: History-dependent percolation in two dimensions
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 study the bond percolation problem under the constraint that the total number of occupied bonds is fixed, so that the canonical ensemble applies. We show via an analytical approach that at criticality, the constraint can induce new…
We investigate percolation on a randomly directed lattice, an intermediate between standard percolation and directed percolation, focusing on the isotropic case in which bonds on opposite directions occur with the same probability. We…
We consider spread-out models of self-avoiding walk, bond percolation, lattice trees and bond lattice animals on the d-dimensional hyper cubic lattice having long finite-range connections, above their upper critical dimensions d=4…
We construct a quantum measure on the power set of non-cyclic oriented graphs of N points, drawing inspiration from 1-dimensional directed percolation. Quantum interference patterns lead to properties which do not appear to have any…
Simulating percolation and critical phenomena of labelled species inside films composed of single-component linear homogeneous macromolecules using molecular Monte Carlo method in 3 dimensions, we study dependence of these conducting…
Percolation is a paradigmatic model in disordered systems and has been applied to various natural phenomena. The percolation transition is known as one of the most robust continuous transitions. However, recent extensive studies have…
We revisit a known model in which (conducting) blocks are hierarchically and randomly deposited on a $d$-dimensional substrate according to a hyperbolic size law with the block size decreasing by a factor $\lambda \, > 1$ in each subsequent…
We study the percolation phase transition on preferential attachment models, in which vertices enter with $m$ edges and attach proportionally to their degree plus $\delta$. We identify the critical percolation threshold as…
Many complex networks exhibit a percolation transition involving a macroscopic connected component, with universal features largely independent of the microscopic model and the macroscopic domain geometry. In contrast, we show that the…
Directed spiral percolation (DSP), percolation under both directional and rotational constraints, is studied on the triangular lattice in two dimensions (2D). The results are compared with that of the 2D square lattice. Clusters generated…
The basic notion of percolation in physics assumes the emergence of a giant connected (percolation) cluster in a large disordered system when the density of connections exceeds some critical value. Until recently, the percolation phase…
The frequency dependence of the dielectric loss angle for a metal-insulator composite was shown previously to be an efficient method to experimentally determine the percolation threshold. The statistical properties of this angle are found…
We study Bernoulli bond percolation on a random recursive tree of size $n$ with percolation parameter $p(n)$ converging to $1$ as $n$ tends to infinity. The sizes of the percolation clusters are naturally stored in a tree. We prove…
A phase diagram for a one dimensional fiber bundle model is constructed with a continuous variation in two parameters guiding dynamics of the model: strength of disorder and system size. We monitor the successive events of fiber rupture in…
We study a random circuit model of constrained fracton dynamics, in which particles on a one-dimensional lattice undergo random local motion subject to both charge and dipole moment conservation. The configuration space of this system…
In this work we consider five different lattice models which exhibit continuous phase transitions into absorbing states. By measuring certain universal functions, which characterize the steady state as well as the dynamical scaling…
The vacant set of random interlacements at level $u>0$, introduced in arXiv:0704.2560, is a percolation model on $\mathbb{Z}^d$, $d \geq 3$ which arises as the set of sites avoided by a Poissonian cloud of doubly infinite trajectories,…
A model named `Colored Percolation' has been introduced with its infinite number of versions in two dimensions. The sites of a regular lattice are randomly occupied with probability $p$ and are then colored by one of the $n$ distinct colors…
A relatively simple and physically transparent model based on quantum percolation and dephasing is employed to construct a global phase diagram which encodes and unifies the critical physics of the quantum Hall, "two-dimensional…