Related papers: Lectures on two-dimensional critical percolation
Lectures given at International School of Physics ``Enrico Fermi'', Varenna, Villa Monastero, June 28-July 7 1994
A modestly revised version of lecture notes that were distributed to accompany my four lectures at the 2017 Spring School of Analysis at Paseky, sponsored by Charles University, Prague. They are an introductory survey of Rubio de Francia…
The dynamical relaxation and scaling properties of three different variants of the contact process in two spatial dimensions are analysed. Dynamical contact processes capture a variety of contagious processes such as the spreading of…
We consider directed percolation processes for particle types A and B coupled unidirectionally by a transmutation reaction A -> B. It is shown that the strong coupling regime of this recently introduced problem defines a universality class…
In this work we use the technique of the partial differential approximants to determine, from a pertubative supercritical series expansion for the ulimate survival probability, the critical line of the contact process model in one dimension…
The close analogy between cluster percolation and string proliferation in the context of critical phenomena is studied. Like clusters in percolation theory, closed strings, which can be either finite-temperature worldlines or topological…
We study the 2d-Ising model defined on finite boxes at temperatures that are below but very close from the critical point. When the temperature approaches the critical point and the size of the box grows fast enough, we establish large…
We present a percolation model that is inspired by recent works on immiscible two-phase flow in a mixed-wet porous medium made of a mixture of grains with two different wettability properties. The percolation model is constructed on a dual…
This is the written version of a set of lectures on perturbative QCD that were delivered to a mixed audience of young theorists and experimentalists in the course of the XXII International Meeting on Fundamental Physics. These notes are…
I describe our understanding of physics near the Planck length, in particular the great progress in the last four years in string theory. These are lectures presented at the 1998 SLAC Summer Institute.
This contribution is relative to the opening lectures of the ISSAOS 2001 summer school and it has the aim to provide the reader with some concepts and techniques concerning chaotic dynamics and transport processes in fluids. Our intention…
We consider high-dimensional percolation at the critical threshold. We condition the origin to be disjointly connected to two points, $x$ and $x'$, and subsequently take the limit as $|x|$, $|x'|$ as well as $|x-x'|$ diverge to infinity.…
I developed the lecture notes based on my ``Causal Inference'' course at the University of California Berkeley over the past seven years. Since half of the students were undergraduates, my lecture notes only required basic knowledge of…
A numerical method is devised for study of stochastic partial differential equations describing directed percolation, the contact process, and other models with a continuous transition to an absorbing state. Owing to the heightened…
We present detailed simulations of a generalization of the Domany-Kinzel model to 2+1 dimensions. It has two control parameters $p$ and $q$ which describe the probabilities $P_k$ of a site to be wetted, if exactly $k$ of its "upstream"…
We continue our study of the chemical (graph) distance inside large critical percolation clusters in dimension two. We prove new estimates, which involve the three-arm probability, for the point-to-surface and point-to-point distances. We…
These are notes based on a series of lectures given at the KITP workshop "Quantum Criticality and the AdS/CFT Correspondence" in July, 2009. The goal of the lectures was to introduce condensed matter physicists to the AdS/CFT…
We consider the percolation problem in the high-temperature Ising model on the two-dimensional square lattice at or near critical external fields. The incipient infinite cluster (IIC) measure in the sense of Kesten is constructed. As a…
The concept of midpoint percolation has recently been applied to characterize the double percolation transitions in negatively curved structures. Regular $d$-dimensional hypercubic lattices are in the present work investigated using the…
In the presence of attraction, the jamming transition of packings of frictionless particles corresponds to the rigidity percolation. When the range of attraction is long, the distribution of the size of rigid clusters, $P(s)$, is continuous…