Related papers: Critical Phenomena: An Introduction from a modern …

We give an introduction to renormalisation, focusing first on a pedagogical description of fundamental concepts of the procedure and its features, then we introduce the renormalisation group and its equations. We discuss then the case of…

These lectures give an introduction to the methods of conformal field theory as applied to deriving certain results in two-dimensional critical percolation: namely the probability that there exists at least one cluster connecting two…

These are introductory lecture notes aimed at beginning graduate students covering fundamental concepts and ideas behind the renormalisation group. Our main goal is to motivate it and then explore its consequences, in the context of quantum…

Several problems in cosmology and astrophysics are described in which critical phenomena of various types may play a role. These include the organization of the disks of spiral galaxies, various aspects of the problem of structure formation…

Recurrence plots exhibit line structures which represent typical behaviour of the investigated system. The local slope of these line structures is connected with a specific transformation of the time scales of different segments of the…

Let a cluster be a term with a number of patterns occurring in it. We give two accounts of clusters, a geometric one as sets of (node and edge) positions, and an inductive one as pairs of terms with gaps (2nd order variables) and…

The standard model of particle physics represents the cornerstone of our understanding of the microscopic world. In these lectures we review its contents and structure, with a particular emphasis on the central role played by symmetries and…

In order to understand the dynamical mechanism of the friction phenomena, we heavily rely on the numerical analysis using various methods: molecular dynamics, Langevin equation, lattice Boltzmann method, Monte Carlo, e.t.c.. We propose a…

The infrared behaviour of a non-mean field spin-glass system is analysed, and the critical exponent related to the divergence of the correlation length is computed at two loops within the epsilon-expansion technique with two independent…

This is an introduction to conformal invariance and two-dimensional critical phenomena for graduate students and condensed-matter physicists. After explaining the algebraic foundations of conformal invariance, numerical methods and their…

This opening editorial aims to interest researchers and encourage novel research in the closely related fields of sociophysics and computational social science. We briefly discuss challenges and possible research directions in the study of…

We have investigated the time series by the mapping them to the complex network. We have studied the behavior of the relative number of clusters in dynamic visibility graphs near the critical value of the angle of view. Time series of…

Many systems involve numerous interacting parts and the whole system can have properties that the individual parts do not. I take this novelty as the defining characteristic of an emergent property. Other characteristics associated with…

Divergence-form operators with random coefficients homogenize over large scales. Over the last decade, an intensive research effort focused on turning this asymptotic statement into quantitative estimates. The goal of this note is to review…

The collapse of man-made and natural structures is a complex phenomenon that has been studied for centuries. We propose a new approach to understanding catastrophic instabilities, based on the idea that they do not occur at the critical…

In physics we attempt to infer the rules governing a system given only the results of imprecise measurements. This is an ill-posed problem because certain features of the system's state cannot be resolved by the measurements. However, by…

When a large number of similar entities interact among each other and with their environment at a low scale, unexpected outcomes at higher spatio-temporal scales might spontaneously arise. This nontrivial phenomenon, known as emergence,…

Emergent patterns in complex systems are related to many intriguing phenomena in modern science and philosophy. Several conceptions such as weak, strong and robust emergence have been proposed to emphasize different epistemological and…

Complex networks are an important paradigm of modern complex systems sciences which allows quantitatively assessing the structural properties of systems composed of different interacting entities. During the last years, intensive efforts…

We consider a class of models of opinion formation where the dissemination of individual opinions occurs through the spreading of local consensus and disagreement. We study the emergence of full collective consensus or maximal disagreement…