Related papers: Renormalization Group and Probability Theory
A non technical introduction to the concept of renormalization is given, with an emphasis on the energy scale dependence in the description of a physical system. We first describe the idea of scale dependence in the study of a ferromagnetic…
We show that the functional renormalization group (FRG) allows for the calculation of the probability distribution function of the sum of strongly correlated random variables. On the example of the three-dimensional Ising model at…
The result from developing and applying the notions of functional self-similarity and the Bogoliubov renormalization group to boundary-value problems in mathematical physics during the last decade are reviewed. The main achievement is the…
Two different models exhibiting self-organized criticality are analyzed by means of the dynamic renormalization group. Although the two models differ by their behavior under a parity transformation of the order parameter, it is shown that…
We explore the applicability of the exact renormalization group to the study of tunnelling phenomena. We investigate quantum-mechanical systems whose energy eigenstates are affected significantly by tunnelling through a barrier in the…
We present a systematic study to test a recently introduced phenomenological renormalization group, proposed to coarse-grain data of neural activity from their correlation matrix. The approach allows, at least in principle, to establish…
Renormalization group, and in particular its Quantum Field Theory implementation has provided us with essential tools for the description of the phase transitions and critical phenomena beyond mean field theory. We therefore review the…
The renormalization group is used to improve the effective potential of massive ${\rm O}(N)$ symmetric $\phi^4$ theory. Explicit results are given at the two-loop level.
The Renormalization Group encodes three concepts that could be key to accelerate progress in quantum gravity. First, it provides a micro-macro connection that could connect microscopic spacetime physics to phenomenology at observationally…
According to the available publications, the field theoretical renormalization group (RG) approach in the two-dimensional case gives the critical exponents that differ from the known exact values. This fact was attempted to explain by the…
The scaling form of the free--energy near a critical point allows for the definition of various universal ratios of thermodynamical amplitudes. Together with the critical exponents they characterize the universality classes and may be…
On the basis of a limited number of reasonable axioms, we discuss the classification of all the possible universality classes of diffeomorphisms invariant metric theories of quantum gravity. We use the language of the renormalization group…
The renormalization-group improved effective potential for an arbitrary renormalizable massless gauge theory in curved spacetime is found,thus generalizing Coleman-Weinberg's approach corresponding to flat space.Some explicit examples are…
Effective field theories provide a suitable framework for both particle physics and statistical physics. We delve deeper into the study of the effective three-dimensional scalar field theory for its application to statistical physics,…
An introduction to the theory of the renormalization group in the context of quantum field theories of relevance to particle physics is presented in the form of 6 lectures delivered to the British Universities Summer School in Theoretical…
A class of exact infinitesimal renormalization group transformations is proposed and studied. These transformations are pure changes of variables (i.e., no integration or elimination of some degrees of freedom is required) such that a…
We study the singularity of the order parameter at the transition between a critical phase and an ordered phase of bond percolation on pointed hierarchical graphs. In pointed hierarchical graphs, the renormalization group (RG) equation…
Extending the usual Ginzburg-Landau theory for the random-field Ising model, the possibility of dimensional reduction is reconsidered. A renormalization group for the probability distribution of magnetic impurities is applied. New…
The concept and technics of real space renormalization group are applied to study majority rule voting in hierarchical structures. It is found that democratic voting can lead to totalitarianism by keeping in power a small minority.…
The running coupling constants are introduced in Quantum Mechanics and their evolution is described by the help of the renormalization group equation.