Related papers: Critical Phenomena: An Introduction from a modern …
Concerning renormalisation group theory applied to phase transitions, we examine the value of positive numerical and analytical evidence, the divergent short-wavelength behaviour of classical free fields and the absence of UV-divergences in…
We present some clues to the study of the renormalization group, at graduate level, as well as some bibliographical pointers to classical resources. Just the kind of things one had liked to hear when starting to study the subject.
In the past two decades or so, we have learned how to understand crackling noise in a wide variety of systems. We review here the basic ideas and methods we use to understand crackling noise - critical phenomena, universality, the…
Phase transitions and critical phenomena are among the most intriguing phenomena in nature and their renormalization-group theory is one of the greatest achievements of theoretical physics. However, the predictions of the theory above an…
The object of this lecture is to propose a series of conjectures and problems in different fields of analysis. They have been formulated with the aim of introducing some innovative methods in the study of classical topics, as open mappings,…
In this short note we discuss recent attempts to describe pre-crash market dynamics with analogies from theory of critical phenomena.
After a brief presentation of the exact renormalization group equation, we illustrate how the field theoretical (perturbative) approach to critical phenomena takes place in the more general Wilson (nonperturbative) approach. Notions such as…
In these lectures I discuss peculiarities of the critical behaviour of ``non-ideal'' systems as it is explained by the renormalization group approach. Examples considered here include account of the single-ion anisotropy, structural…
We consider emergence from the perspective of dynamics: states of a system evolving with time. We focus on the role of a decomposition of wholes into parts, and attempt to characterize relationships between levels without reference to…
I explain the methods that are used in field theory for problems involving typical momenta on two or more widely disparate scales. The principal topics are: (a) renormalization, which treats the problem of taking an ultra-violet cut-off to…
Many complex systems are representable as macroscopic set of elements which interact by simple rules. The complex macroscopically relevant phenomena are then the result of the generic emergence of a space-time multi-scale dynamics. Critical…
Different perturbation theory treatments of the Ginzburg-Landau phase transition model are discussed. This includes a criticism of the perturbative renormalization group (RG) approach and a proposal of a novel method providing critical…
An introduction into the theory of boundary critical phenomena and the application of the field-theoretical renormalization group method to these is given. The emphasis is on a discussion of surface critical behavior at bulk critical points…
The renormalization group has played an important role in the physics of the second half of the twentieth century both as a conceptual and a calculational tool. In particular it provided the key ideas for the construction of a qualitative…
We present a calculation of critical phenomena directly in continuous dimension d employing an exact renormalization group equation for the effective average action. For an Ising-type scalar field theory we calculate the critical exponents…
We review some results on the critical phenomena in the Dyson hierarchical model and renormalization group.
The last decade has witnessed a number of important and exciting developments that had been achieved for improving recurrence plot based data analysis and to widen its application potential. We will give a brief overview about important and…
An elementary introduction to perturbative renormalization and renormalization group is presented. No prior knowledge of field theory is necessary because we do not refer to a particular physical theory. We are thus able to disentangle what…
Under quite general conditions critical phenomena can be described with high order linked cluster expansions. The coefficients of the series admit a graphical expansion that is generated with the aid of computers. Our generalization of…
The "universality" of critical phenomena is much discussed in philosophy of scientific explanation, idealizations and philosophy of physics. Lange and Reutlinger recently opposed Batterman concerning the role of some deliberate distortions…