Related papers: Critical phenomena in the Dyson hierarchical model…
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…
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…
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…
The Renormalization Group (RG) methods are still far from being completely understood in quenched disordered systems. In order to gain insight into the nature of the phase transition of these systems, it is common to investigate simple…
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…
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…
A short review of recent renormalization group analyses of the self-consistence of the Standard Model is presented.
We have studied the one dimensional Dyson hierarchical model in presence of a random field. This is a long range model where the interactions scale with the distance with a power law-like form J(r) ~ r^{-\rho} and we can explore mean field…
A classification of critical behavior is provided in systems for which the renormalization group equations are control-parameter dependent. It describes phase transitions in networks with a recursive, hierarchical structure but appears to…
The phenomenological renormalization group (PRG) has been applied to the study of scaleinvariant phenomena in neuronal data, providing evidence for critical phenomena in the brain. However, it remains unclear how reliably these observed…
We review the theory of renormalization, including perturbative renormalization, regularized functional integrals, Renormalization Group and rigorous renormalization.
We review results concerning the critical behavior of spin systems at equilibrium. We consider the Ising and the general O($N$)-symmetric universality classes, including the $N\to 0$ limit that describes the critical behavior of…
Our aim in this set of lectures is to give an introduction to critical phenomena that emphasizes the emergence of and the role played by diverging length-scales. It is now accepted that renormalization group gives the basic understanding of…
We review the theoretical description of the random field Ising and $O(N)$ models obtained from the functional renormalization group, either in its nonperturbative implementation or, in some limits, in perturbative implementations. The…
We employ the machinery of smooth scaling and coarse-graining of observables, developed recently by us in the context of so-called fluctuation operators (inspired by prior work of Verbeure et al) to make a rigorous renormalisation group…
Some renormalization group approaches have been proposed during the last few years which are close in spirit to the Nightingale phenomenological procedure. In essence, by exploiting the finite size scaling hypothesis, the approximate…
Various uses of the renormalization group are examined.
The Dyson hierarchical version of the quantum Ising chain with Long-Ranged power-law ferromagnetic couplings $J(r) \propto r^{-1-\sigma}$ and pure or random transverse fields is studied via real-space renormalization. For the pure case, 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…
It is shown that the presence of multiple time scales at a quantum critical point can lead to a breakdown of the loop expansion for critical exponents, since coefficients in the expansion diverge. Consequently, results obtained from…