Related papers: Universality for bond percolation in two dimension…
Extensive Monte-Carlo simulations were performed to study bond percolation on the simple cubic (s.c.), face-centered cubic (f.c.c.), and body-centered cubic (b.c.c.) lattices, using an epidemic kind of approach. These simulations provide…
In this paper we study monotone cellular automata in $d$ dimensions. We develop a general method for bounding the growth of the infected set when the initial configuration is chosen randomly, and then use this method to prove a lower bound…
We obtain the exact solution of the bond-percolation thresholds with inhomogenous probabilities on the square lattice. Our method is based on the duality analysis with real-space renormalization, which is a profound technique invented in…
We prove up-to-constants bounds on the two-point function (i.e., point-to-point connection probabilities) for critical long-range percolation on the $d$-dimensional hierarchical lattice. More precisely, we prove that if we connect each pair…
The number of clusters per site $n(p)$ in percolation at the critical point $p = p_c$ is not itself a universal quantity---it depends upon the lattice and percolation type (site or bond). However, many of its properties, including…
Extended-range percolation on various regular lattices, including all eleven Archimedean lattices in two dimensions, and the simple cubic (SC), body-centered cubic (BCC), and face-centered cubic (FCC) lattices in three dimensions, is…
We reinvestigate the 2D problem of the inhomogeneous incipient infinite cluster where, in an independent percolation model, the density decays to p_c with an inverse power, \lambda, of the distance to the origin. Assuming the existence of…
The shape-dependent universality of the excess percolation cluster number and cross-configuration probability on a torus is discussed. Besides the aspect ratio of the torus, the universality class depends upon the twist in the periodic…
We study a large class of Bernoulli percolation models on random lattices of the half- plane, obtained as local limits of uniform planar triangulations or quadrangulations. We first compute the exact value of the site percolation threshold…
We consider a class of percolation models where the local occupation variables have long-range correlations decaying as a power law $\sim r^{-a}$ at large distances $r$, for some $0< a< d$ where $d$ is the underlying spatial dimension. For…
Zhang found a simple, elegant argument deducing the non-existence of an infinite open cluster in certain lattice percolation models (for example, p=1/2 bond percolation on the square lattice) from general results on the uniqueness of an…
We discuss a class of critical models in d>1+1 dimensions whose electrical conductivity and charge susceptibility are fixed by the central charge in a universal manner. We comment on possible bounds on conductivity, as suggested by…
A problem of the crossover from percolation to diffusion transport is considered. A general scaling theory is proposed. It introduces phenomenologically four critical exponents which are connected by two equations. One exponent is…
We show that a superposition of an $\varepsilon$-Bernoulli bond percolation and any everywhere percolating subgraph of $\mathbb Z^d$, $d\ge 2$, results in a connected subgraph, which after a renormalization dominates supercritical Bernoulli…
We introduce and study a family of 2D percolation systems which are based on the bond percolation model of the triangular lattice. The system under study has local correlations, however, bonds separated by a few lattice spacings act…
We consider isoperimetric sets, i.e., sets with minimal vertex boundary for a prescribed volume, of the infinite cluster of supercritical site percolation on the triangular lattice. Let $p$ be the percolation parameter and let $p_c$ be the…
Critical exponents characterize the divergent scaling of thermodynamic quantities near phase transitions and allow for the classification of physical systems into universality classes. While quantum gases thermalizing by interparticle…
We study a variation of the dynamic universality class of model H in a spatial dimension of $d=4-\epsilon$, by frustrating charge diffusion and momentum density fluctuations along $d_T=1$ or $d_T=2$ dimensions, while keeping the same…
In a recent paper (arXiv:0911.2514), one of us (FYW) considered the Potts model and bond and site percolation on two general classes of two-dimensional lattices, the triangular-type and kagome-type lattices, and obtained closed-form…
An universal invariant for site and bond percolation thresholds (p_{cs} and p_{cb} respectively) is proposed. The invariant writes {p_{cs}}^{1/a_s}{p_{cb}}^{-1/a_b}=\delta/d where a_s, a_b and \delta are positive constants,and d the space…