Related papers: The random geometry of equilibrium phases
During the past two decades, percolation has long served as a basic paradigm for network resilience, community formation and so on in complex systems. While the percolation transition is known as one of the most robust continuous…
Percolation clusters are random fractals whose geometrical and transport properties can be characterized with the help of probability distribution functions. Using renormalized field theory, we determine the asymptotic form of various of…
This article is preface to the SIGMA special issue "Tensor Models, Formalism and Applications", http://www.emis.de/journals/SIGMA/Tensor_Models.html. The issue is a collection of eight excellent, up to date reviews on random tensor models.…
We study a one parameter family of random graph models that spans a continuum between traditional random graphs of the Erd\H{o}s-R\'enyi type, where there is no underlying structure, and percolation models, where the possible edges are…
This article is a draft of a book chapter of the book entitled "Quantum Percolation and Breakdown", to appear 2008.
We consider here probabilistic models of transportation flows. The main goal of this introduction is rather not to present various techniques for problem solving but to present some intuition to invent adequate and natural models having…
We present a review of nonequilibrium phase transitions in mass-transport models with kinetic processes like fragmentation, diffusion, aggregation, etc. These models have been used extensively to study a wide range of physical problems. We…
We provide a self-contained introduction to random matrices. While some applications are mentioned, our main emphasis is on three different approaches to random matrix models: the Coulomb gas method and its interpretation in terms of…
In this review, a model (the Random Coupling Model) that gives a statistical description of the coupling of radiation into and out of large enclosures through localized and/or distributed channels is presented. The Random Coupling Model…
This short review covers a wide selection of topics from a multidisciplinary area of dynamics of nonequilibrium systems in physics, chemistry, biology. Theoretical models of colloid particle and protein deposition and adhesion at surfaces,…
We develop a statistical mechanics approach for random networks with uncorrelated vertices. We construct equilibrium statistical ensembles of such networks and obtain their partition functions and main characteristics. We find simple…
The study of random graphs has become very popular for real-life network modeling such as social networks or financial networks. Inhomogeneous long-range percolation (or scale-free percolation) on the lattice $\mathbb Z^d$, $d\ge1$, is a…
The present work introduces an efficient Monte Carlo algorithm for continuum percolation composed of randomly-oriented rectangles. By conducting extensive simulations, we report high precision percolation thresholds for a variety of…
A class of nonequilibrium models with short-range interactions and sequential updates is presented. The models describe one dimensional growth processes which display a roughening transition between a smooth and a rough phase. This…
Stochastic differential equations have proved to be a valuable governing framework for many real-world systems which exhibit ``noise'' or randomness in their evolution. One quality of interest in such systems is the shape of their…
The properties of excited nuclear matter and the quest for a phase transition which is expected to exist in this system are the subject of intensive investigations. High energy nuclear collisions between finite nuclei which lead to matter…
We investigate the static and dynamic properties of a celebrated model of social segregation, providing a complete explanation of the mechanisms leading to segregation both in one- and two-dimensional systems. Standard statistical physics…
The percolation, Ising, and O($n$) models constitute fundamental systems in statistical and condensed matter physics. For short-range-interacting cases, the nature of their phase transitions is well established by renormalization-group…
Percolation is perhaps the simplest example of a process exhibiting a phase transition and one of the most studied phenomena in statistical physics. The percolation transition is continuous if sites/bonds are occupied independently with the…
Contents: 1.- Introduction 2.- Scaling of entanglement in (1+1)-dimensional systems 3.- Entanglement and RG-flows 4.- Matrix Product States Appendix A.- Entanglement and order relations B.- Hilbert space in a conformal theory