Related papers: Anchored Critical Percolation Clusters and 2-D Ele…
We investigate the scaling of the largest critical percolation cluster on a large d-dimensional torus, for nearest-neighbor percolation in high dimensions, or when d>6 for sufficient spread-out percolation. We use a relatively simple…
Rigidity Percolation is a crucial framework for describing rigidity transitions in amorphous systems. We present a new, efficient algorithm to study central-force Rigidity Percolation in two dimensions. This algorithm combines the Pebble…
Theory of one-electron transition density matrices has been formulated within the time-independent coupled cluster method for the polarization propagator [R. Moszynski, P. S. \.Zuchowski, and B. Jeziorski, Coll. Czech. Chem. Commun. {\bf…
Monte Carlo computer simulations of a quasi two dimensional (2D) dipolar fluid at low and intermediate densities indicate that the structure of the fluid is well described by an ideal mixture of self-assembling clusters. A detailed analysis…
Motivated by the success of a k-clique percolation method for the identification of overlapping communities in large real networks, here we study the k-clique percolation problem in the Erdos-Renyi graph. When the probability p of two nodes…
Using the AdS/CFT correspondence, we probe the scale-dependence of thermalization in strongly coupled field theories following a quench, via calculations of two-point functions, Wilson loops and entanglement entropy in d=2,3,4. In the…
We develop a cluster expansion for the probability of full connectivity of high density random networks in confined geometries. In contrast to percolation phenomena at lower densities, boundary effects, which have previously been largely…
In two space dimensions, the percolation point of the pure-site clusters of the Ising model coincides with the critical point T_c of the thermal transition and the percolation exponents belong to a special universality class. By introducing…
A relaxed version of Gummelt's covering rules for the aperiodic decagon is considered, which produces certain random-tiling-type structures. These structures are precisely characterized, along with their relationships to various other…
A new site percolation model, directed spiral percolation (DSP), under both directional and rotational (spiral) constraints is studied numerically on the square lattice. The critical percolation threshold $p_c\approx 0.655$ is found between…
Let M_n denote the number of sites in the largest cluster in critical site percolation on the triangular lattice inside a box side length n. We give lower and upper bounds on the probability that M_n / E(M_n) > x of the form exp(- C…
Long range electrostatic, induction and dispersion coefficients including terms of order $R^{-8}$ have been calculated by the sum over states method using time dependent density functional theory. We also computed electrostatic moments and…
Roles of electron correlation effects in the determination of attachment energies, magnetic dipole hyperfine structure constants and electric dipole (E1) matrix elements of the low-lying states in the singly charged cadmium ion (Cd$^+$)…
We have studied electron correlations in the doped two-dimensional (2D) Hubbard model by using the coupled-cluster method (CCM) to investigate whether or not the method can be applied to correct the independent particle approximations…
The statistical behavior of the size (or mass) of the largest cluster in subcritical percolation on a finite lattice of size $N$ is investigated (below the upper critical dimension, presumably $d_c=6$). It is argued that as $N \to \infty$…
Critical systems have always intrigued physicists and precipitated the development of new techniques. Recently, there has been renewed interest in the information contained in their classical configurations, whose computation do not require…
We consider the simple random walk on the infinite cluster of a general class of percolation models on $\mathbb{Z}^d$, $d\geq 3$, including Bernoulli percolation as well as models with strong, algebraically decaying correlations. For almost…
An analysis of water clustering is used to study the quasi-2D percolation transition of water adsorbed at planar hydrophilic surfaces. Above the critical temperature of the layering transition (quasi-2D liquid-vapor phase transition of…
Percolation phenomena of homopolymer brushes on a planar substrate are simulated using the molecular Monte Carlo method in 3 dimensions. The grafted polymers are isolated from each other at extremely low grafting density, whereas a…
We conjecture an exact form for an universal ratio of four-point cluster connectivities in the critical two-dimensional $Q$-color Potts model. We also provide analogous results for the limit $Q\rightarrow 1$ that corresponds to percolation…