相关论文: The random geometry of equilibrium phases

Phase separation is a fairly common physical phenomenon with examples including the formation of water droplets from humid air (fog, rain), the separation of a crystalline structure from an isotropic material such as a liquid or even the…

Random shapes arise naturally in many contexts. The topological and geometric structure of such objects is interesting for its own sake, and also for applications. In physics, for example, such objects arise naturally in quantum gravity, in…

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…

We introduce a set of iterative equations that exactly solves the size distribution of components on small arbitrary graphs after the random removal of edges. We also demonstrate how these equations can be used to predict the distribution…

We study nonequilibrium phase transitions of reaction-diffusion systems defined on randomly diluted lattices, focusing on the transition across the lattice percolation threshold. To develop a theory for this transition, we combine classical…

The past two decades have witnessed a surge of new research in the analysis of randomized experiments. The emergence of this literature may seem surprising given the widespread use and long history of experiments as the "gold standard" in…

The methods of conformal field theory are used to compute the crossing probabilities between segments of the boundary of a compact two-dimensional region at the percolation threshold. These probabilities are shown to be invariant not only…

The paper is devoted to the questions connected with the investigation of the S.P. Novikov problem of the description of the geometry of level lines of quasiperiodic functions on a plane with different numbers of quasiperiods. We consider…

This is a brief introduction to the statistical theory of fluid turbulence, with an emphasis on the field-theoretic treatment of renormalized viscosity and energy fluxes.

In this work, we study the percolation transition and large deviation properties of generalized canonical network ensembles. This new type of random networks might have a very rich complex structure, including high heterogeneous degree…

Percolation models describe the inside of a porous material. The theory emerged timidly in the middle of the twentieth century before becoming one of the major objects of interest in probability and mathematical physics. The golden age of…

In many real network systems, nodes usually cooperate with each other and form groups, in order to enhance their robustness to risks. This motivates us to study a new type of percolation, group percolation, in interdependent networks under…

Percolation and synchronization are two phase transitions that have been extensively studied since already long ago. A classic result is that, in the vast majority of cases, these transitions are of the second-order type, i.e. continuous…

The percolating phase of whatever random percolation process resembles the confining vacuum of a gauge theory in most respects, with a string tension having a well-behaved continuum limit, a non trivial glueball spectrum and a deconfinement…

In this chapter we review concepts and theories of polymer dynamics. We think of it as an introduction to the topic for scientists specializing in other subfields of statistical mechanics and condensed matter theory, so, for the readers…

Progress in the research area of colloidal dispersions in external fields within the last years is reviewed. Colloidal dispersions play a pivotal role as model systems for phase transitions in classical statistical mechanics. In recent…

We discuss several algorithms for sampling from unnormalized probability distributions in statistical physics, but using the language of statistics and machine learning. We provide a self-contained introduction to some key ideas and…

Topological phases of matter are often understood and predicted with the help of crystal symmetries, although they don't rely on them to exist. In this chapter we review how topological phases have been recently shown to emerge in amorphous…

The random-cluster model, a correlated bond percolation model, unifies a range of important models of statistical mechanics in one description, including independent bond percolation, the Potts model and uniform spanning trees. By…

The aim of these notes is to give a quick introduction to FK-percolation, focusing on certain recent results about the phase transition of the two dimensional model, namely its continuity or discontinuity depending on the cluster weight…