Related papers: Lectures on two-dimensional critical percolation
I summarize the highlights of "Cosmic Flows: Towards an Understanding of the Large-scale Structure in the Universe", a workshop held in Victoria, Canada in July 1999.
The probabilities of clusters spanning a hypercube of dimensions two to seven along one axis of a percolation system under criticality were investigated numerically. We used a modified Hoshen--Kopelman algorithm combined with Grassberger's…
These lectures were prepared for the 2014 PCMI graduate summer school and were designed to be a lightweight introduction to statistical mechanics for mathematicians. The applications feature some of the themes of the summer school: sphere…
We study the geometry of the critical clusters in fully coordinated percolation on the square lattice. By Monte Carlo simulations (static exponents) and normal mode analysis (dynamic exponents), we find that this problem is in the same…
Despite great progress in the study of critical percolation on $\mathbb{Z}^d$ for $d$ large, properties of critical clusters in high-dimensional fractional spaces and boxes remain poorly understood, unlike the situation in two dimensions.…
Following an introduction which explains some basic ideas about diffraction, the semiclassical approach to diffraction in deep inelastic scattering (DIS) is outlined. Some phenomenological tests of this picture, concerning the $p_{\perp}$…
The fractal structure and scaling properties of a 2d slice of the 3d Ising model is studied using Monte Carlo techniques. The percolation transition of geometric spin (GS) clusters is found to occur at the Curie point, reflecting the…
These notes are an account of a series of lectures given at the Les Houches Summer School "Active Matter and Non-equilibrium Statistical Physics" during August and September 2018. The lectures can be viewed online at…
These notes are part of the research seminar with title "Theory of Bergman spaces and related function spaces" that took place in the University of Crete, Department of Mathematics (September 2006- December 2007), in the framework of the…
Science communication skills are considered essential learning objectives for undergraduate physics students. However, high enrollment and limited class resources present significant barriers to providing students ample opportunities to…
Recently it was conjectured that nodal domains of random wave functions are adequately described by critical percolation theory. In this paper we strengthen this conjecture in two respects. First, we show that, though wave function…
We prove the existence of non-trivial phase transitions for the intersection of two independent random interlacements and the complement of the intersection. Some asymptotic results about the phase curves are also obtained. Moreover, we…
The pair contact process with diffusion is studied by means of multispin Monte Carlo simulations and density matrix renormalization group calculations. Effective critical exponents are found to behave nonmonotonically as functions of time…
In this paper we propose the Ising model to study the propagation of water in 2 dimensional (2D) petroleum reservoir in which each bond between its pores has the probability $p$ of being activated. We analyze the water movement pattern in…
These notes are loosely based on lectures given at the CERN Winter School on Supergravity, Strings and Gauge theories, February 2009 and at the IPM String School in Tehran, April 2009. I have focused on a few concrete topics and also on…
We apply connectedness percolation theory to fractal liquids of hard particles, and make use of a Percus-Yevick liquid state theory combined with a geometric connectivity criterion. We find that in fractal dimensions the percolation…
Lectures given at the summer school on Algebraic Groups, Goettingen, June 27 - July 15 2005
These extended notes are based on a series of six lectures presented at the summer school ``Cohomology of groups and algebraic $K$-theory'' which took place in Hangzhou, China from July 1 until July 12 in 2007. They give an introduction to…
We expect that the experimental study of percolation cluster formation and appearance of the critical transparency of the strongly interacting matter can give the information about the onset state of deconfinement.
These are lecture notes of the 51st Saint-Flour summer school, July 2023, on the topic of Bayesian nonparametric statistics