Related papers: Percolation with long-range correlated disorder
The properties of the pure-site clusters of spin models, i.e. the clusters which are obtained by joining nearest-neighbour spins of the same sign, are here investigated. In the Ising model in two dimensions it is known that such clusters…
In this paper it presents, develops and discusses the existence of a process with long scope memory structure, representing of the independence between the degree of randomness of the traffic generated by the sources and flow pattern…
We study the percolation of strongly connected clusters (SCCs), in which sites are mutually reachable through directed paths, in systems with randomly oriented bonds by extensive simulations on hypercubic lattices from dimension $d=2$ to…
We study the percolative properties of bi-dimensional systems generated by a random sequential adsorption of line-segments on a square lattice. As the segment length grows, the percolation threshold decreases, goes through a minimum and…
We propose a fluctuation analysis to quantify spatial correlations in complex networks. The approach considers the sequences of degrees along shortest paths in the networks and quantifies the fluctuations in analogy to time series. In this…
We study diffusion on a substrate with permanent traps distributed with critical positional correlation, modeled by their placement on the perimeters of a critical percolation cluster. We perform a numerical analysis of the vibrational…
We investigate operator dynamics and entanglement growth in dual-unitary circuits, a class of locally scrambled quantum systems that enables efficient simulation beyond the exponential complexity of the Hilbert space. By mapping the…
We study bond percolation of $N$ non-interacting Gaussian polymers of $\ell$ segments on a 2D square lattice of size $L$ with reflecting boundaries. Through simulations, we find the fraction of configurations displaying {\em no} connected…
The simplest transport problem, namely maxflow, is investigated on critical percolation clusters in two and three dimensions, using a combination of extremal statistics arguments and exact numerical computations, for power-law distributed…
The influence of geometry and morphology of superconducting structure on critical currents and magnetic flux trapping in percolative type-II superconductor is considered. The superconductor contains the clusters of a normal phase, which act…
We study hierarchical network models which have recently been introduced to approximate the Chalker-Coddington model for the integer quantum Hall effect (A.G. Galstyan and M.E. Raikh, PRB 56 1422 (1997); Arovas et al., PRB 56, 4751 (1997)).…
Critical properties of hulls of directed spiral percolation (DSP) clusters are studied on the square and triangular lattices in two dimensions (2D). The hull fractal dimension ($d_H$) and some of the critical exponents associated with…
We study classical percolation models in Fock space as proxies for the quantum many-body localisation (MBL) transition. Percolation rules are defined for two models of disordered quantum spin-chains using their microscopic quantum…
A geometric approach to critical fluctuations of a nonequilibrium model is reported. The two-dimensional majority vote model was investigated by Monte Carlo simulations on square lattices of various sizes and a detailed scaling analysis of…
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…
In a Monte Carlo study the conductivity of two-dimensional random stick systems is investigated from the percolation threshold up to ten times the percolation threshold density. We propose a model explicitly depending on the stick density…
Numerical simulations of Diffusion-Limited and Reaction-Limited Cluster-Cluster Aggregation processes of identical particles are performed in a two-dimensional box. It is shown that, for concentrations larger than a characteristic gel…
This paper studies the critical and near-critical regimes of the planar random-cluster model on $\mathbb Z^2$ with cluster-weight $q\in[1,4]$ using novel coupling techniques. More precisely, we derive the scaling relations between the…
We study gradient percolation for site percolation on the triangular lattice. This is a percolation model where the percolation probability depends linearly on the location of the site. We prove the results predicted by physicists for this…
We study the flow of fluid in porous media in dimensions $d=2$ and 3. The medium is modeled by bond percolation on a lattice of $L^d$ sites, while the flow front is modeled by tracer particles driven by a pressure difference between two…