Related papers: Self-Consistent Scaling Theory for Logarithmic Cor…
This work is dedicated to the study of both large-$N$ and perturbative quantum behaviors of Lifshitz nonlinear sigma models with dynamical critical exponent $z=2$ in 2+1 dimensions. We discuss renormalization and renormalization group…
Fluctuating hydrodynamics is used to describe the total energy fluctuations of a freely evolving gas of inelastic hard spheres near the threshold of the clustering instability. They are shown to be governed by vorticity fluctuations only,…
Log-periodic amplitudes appear in the critical behavior of a large class of systems, in particular when a discrete scale invariance is present. Here we show how to compute these critical amplitudes perturbatively when they originate from a…
Statistical physics is used to investigate independent component analysis with polynomial contrast functions. While the replica method fails, an adapted cavity approach yields valid results. The learning curves, obtained in a suitable…
We numerically exhibit strange scaling and temporal evolution of finite-size fluctuation in thermal equilibrium of a simple long-range interacting system. These phenomena are explained from the view point of existence of the Casimirs and…
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…
It is often assumed that for treating numerical (or experimental) data on continuous transitions the formal analysis derived from the Renormalization Group Theory can only be applied over a narrow temperature range, the "critical region";…
Percolation is a cornerstone concept in physics, providing crucial insights into critical phenomena and phase transitions. In this study, we adopt a kinetic perspective to reveal the scaling behaviors of higher-order gaps in the largest…
The error autocorrection effect means that in a calculation all the intermediate errors compensate each other, so the final result is much more accurate than the intermediate results. In this case standard interval estimates are too…
This paper discusses the mathematical representation of an empirically observed phenomenon, referred to as Incremental Similarity. We discuss this feature from the viewpoint of stochastic processes and present a variety of non-trivial…
We deal with the random combinatorial structures called assemblies. By weakening the logarithmic condition which assures regularity of the number of components of a given order, we extend the notion of logarithmic assemblies. Using the…
Wall turbulence has a sublayer where one-point statistics, e.g., the mean velocity and the variances of some velocity fluctuations, vary logarithmically with the distance from the wall. This logarithmic scaling is found here for two-point…
Recent work on exact renormalization group flow equations has pointed out the possibility to study critical phenomena in continuous dimension D of space. In an investigation of the O(N) model the dimension N of the fields may be seen as a…
The results of the renormalization group are commonly advertised as the existence of power law singularities near critical points. The classic predictions are often violated and logarithmic and exponential corrections are treated on a…
We propose a picture of stock market crashes as critical points in a hierachical system with discrete scaling. The critical exponent is then complex, leading to log-periodic fluctuations in stock market indexes. We present ``experimental''…
Thermal fluctuations are a fundamental feature of dissipative systems that are essential for understanding physics near the expected critical point of QCD and in small systems. When such fluctuations are modeled naively in relativistic…
One way to resolve the actuation problem of metaphorical language change is to provide a statistical profile of metaphorical constructions and generative rules with antecedent conditions. Based on arguments from the view of language as…
Within wall turbulence, there is a sublayer where the mean velocity and the variance of velocity fluctuations vary logarithmically with the height from the wall. This logarithmic scaling is also known for the mean concentration of a passive…
We obtain logarithmic behaviours of a four-point correlation function in the c=-2 conformal field theory by using the Feigin-Fuchs construction. It becomes an indeterminate form by a naive evaluation, but is obtained by introducing an…
Exactly solvable models of planar polygons, weighted by perimeter and area, have deepened our understanding of the critical behaviour of polygon models in recent years. Based on these results, we derive a conjecture for the exact form of…