Related papers: The random geometry of equilibrium phases
This paper exposes a novel exploratory formalism, which end goal is the numerical simulation of the dynamics of a cloud of particles weakly or strongly coupled with a turbulent fluid. Giventhe large panel of expertise of the list of…
A brief introduction to the technique of Monte Carlo simulations in statistical physics is presented. The topics covered include statistical ensembles random and pseudo random numbers, random sampling techniques, importance sampling, Markov…
Index: 1) Trajectories, distributions and path integrals. 2) Time-reversal and Equilibrium 3) Separation of timescales 4) Large Deviations 5) Metastability and dynamical phase transitions 6) Fluctuation Theorems and Jarzynski equality
We describe the percolation model and some of the principal results and open problems in percolation theory. We also discuss briefly the spectacular recent progress by Lawler, Schramm, Smirnov and Werner towards understanding the phase…
Interdependent networks are ubiquitous in our society, ranging from infrastructure to economics, and the study of their cascading behaviors using percolation theory has attracted much attention in the recent years. To analyze the…
For Encyclopedia of Complexity and Systems Science (Springer Verlag). No abstract. I. Definition and Introduction II. Methods III. Quantities and Exponents IV. Fractal Dimension; Incipient Infinite Cluster V. Simple Renormalisation Group…
Recently, it has been recognized that phase transitions play an important role in the probabilistic analysis of combinatorial optimization problems. However, there are in fact many other relations that lead to close ties between computer…
An overview is given of recent advances in nonequilibrium statistical mechanics about the statistics of random paths and current fluctuations. Although statistics is carried out in space for equilibrium statistical mechanics, statistics is…
This chapter provides a tutorial overview of first principles methods to describe the properties of matter at the ground state or equilibrium. It begins with a brief introduction to quantum and statistical mechanics for predicting the…
This book chapter introduces to the concept of weak chaos, aspects of its ergodic theory description, and properties of the anomalous dynamics associated with it. In the first half of the chapter we study simple one-dimensional…
The continuum random cluster model is a Gibbs modification of the standard boolean model of intensity $z > 0$ and law of radii $Q$. The formal unormalized density is given by $q^{N_{cc}}$ where $q$ is a fixed parameter and $N_{cc}$ is the…
We describe a random matrix approach that can provide generic and readily soluble mean-field descriptions of the phase diagram for a variety of systems ranging from QCD to high-T_c materials. Instead of working from specific models, phase…
We present and investigate an extension of the classical random graph to a general class of inhomogeneous random graph models, where vertices come in different types, and the probability of realizing an edge depends on the types of its…
In self-gravitating stars, two dimensional or geophysical flows and in plasmas, long range interactions imply a lack of additivity for the energy; as a consequence, the usual thermodynamic limit is not appropriate. However, by contrast with…
Recent results concerning the topological properties of random geometrical sets have been successfully applied to the study of the morphology of clusters in percolation theory. This approach provides an alternative way of inspecting the…
This is a survey article to be part of the Encyclopedia of Mathematical Physics, to be published by Elsevier in the beginning of 2006.
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…
We review the field theory approach to percolation processes. Specifically, we focus on the so-called simple and general epidemic processes that display continuous non-equilibrium active to absorbing state phase transitions whose asymptotic…
This is a set of four lectures devoted to simple ideas about turbulent transport, a ubiquitous non-equilibrium phenomenon. In the course similar to that given by the author in 2006 in Warwick [45], we discuss lessons which have been learned…
This statistical physics thesis focuses on the study of three kinds of systems which display repulsive interactions: eigenvalues of random matrices, non-crossing random walks and trapped fermions. These systems share many links, which can…