Related papers: Universal scaling relations for logarithmic-correc…
We show how to combine Kesten's scaling relations, the determination of critical exponents associated to the stochastic Loewner evolution process by Lawler, Schramm, and Werner, and Smirnov's proof of Cardy's formula, in order to determine…
An analytic perturbation theory is suggested in order to find finite-size corrections to the scaling power laws. In the frame of this theory it is shown that the first order finite-size correction to the scaling power laws has following…
We present a random-matrix realization of a two-dimensional percolation model with the occupation probability $p$. We find that the behavior of the model is governed by the two first extreme eigenvalues. While the second extreme eigenvalue…
Complex systems consist of many interacting elements which participate in some dynamical process. The activity of various elements is often different and the fluctuation in the activity of an element grows monotonically with the average…
The dynamic properties of a classical tracer particle in a random, disordered medium are investigated close to the localization transition. For Lorentz models obeying Newtonian and diffusive motion at the microscale, we have performed…
The critical point of a topological phase transition is described by a conformal field theory, where finite-size corrections to energy are uniquely related to its central charge. We investigate the finite-size scaling away from criticality…
The most general form of a marginal extended perturbation in a two-dimensional system is deduced from scaling considerations. It includes as particular cases extended perturbations decaying either from a surface, a line or a point for which…
Publicly traded companies are fundamental units of contemporary economies and markets and are important mechanisms through which humans interact with their environments. Understanding the general properties that underlie the processes of…
At a continuous transition into a nonunique absorbing state, particle systems may exhibit nonuniversal critical behavior, in apparent violation of hyperscaling. We propose a generalized scaling theory for dynamic critical behavior at a…
A consistent generalization of statistical mechanics is obtained by applying the maximum entropy principle to a trace-form entropy and by requiring that physically motivated mathematical properties are preserved. The emerging…
We study continuum percolation of overlapping circular discs of two sizes. We propose a phenomenological scaling equation for the increase in the effective size of the larger discs due to the presence of the smaller discs. The critical…
Scale invariance is a central organizing principle in physics, underlying phenomena that range from critical behaviour in statistical mechanics to transport and chaos in nonlinear dynamical systems. Here we present a unified and physically…
We discuss the concept of discrete scale invariance and how it leads to complex critical exponents (or dimensions), i.e. to the log-periodic corrections to scaling. After their initial suggestion as formal solutions of renormalization group…
Universality is a common quality in different physical parameters that is rooted in the deep nature of physical systems. Scaling relation is a typical universality for critical phenomena around a quantum phase transition, while topological…
Control for confounders in observational studies was generally handled through stratification and standardization until the 1960s. Standardization typically reweights the stratum-specific rates so that exposure categories become comparable.…
Critical transitions are observed in many complex systems. This includes the onset of synchronization in a network of coupled oscillators or the emergence an epidemic state within a population. "Explosive" first-order transitions have…
Phase transitions are divided into first-order phase transitions and continuous ones in current classification. While the latter shows striking phenomena of scaling and universality, the former is generically characterized by discontinuous…
We study the 3d Ising universality class using the functional renormalisation group. With the help of background fields and a derivative expansion up to fourth order we compute the leading index, the subleading symmetric and anti-symmetric…
We define geometric critical exponents for systems that undergo continuous second order classical and quantum phase transitions. These relate scalar quantities on the information theoretic parameter manifolds of such systems, near…
We study the depinning transitions of elastic strings in disordered media in two different cases. We consider the elastic forces to be of infinite range in one case, where the magnitude is proportional to the extension of the string. The…