Related papers: Approximate solutions of exact renormalization gro…
We develop a systematic multi-local expansion of the Polchinski-Wilson exact renormalization group (ERG) equation. Integrating out explicitly the non local interactions, we reduce the ERG equation obeyed by the full interaction functional…
The validity of the renormalization group approach for large $N$ is clarified by using the vector model as an example. An exact difference equation is obtained which relates free energies for neighboring values of $N$. The reparametrization…
Perturbative renormalization group theory is developed as a unified tool for global asymptotic analysis. With numerous examples, we illustrate its application to ordinary differential equation problems involving multiple scales, boundary…
The effective average actions for gauge theories and the associated nonperturbative evolution equations which govern their renormalization group flow are reviewed and various applications are described. As an example of a topological field…
We use the functional renormalization group equation for the effective average action to study the fixed point structure of gravity-fermion systems on a curved background spacetime. We approximate the effective average action by the…
In this paper, we review some general formulations of exact renormalisation group equations and loop equations for tensor models and tensorial group field theories. We illustrate the use of these equations in the derivation of the leading…
We study the effective theory of the conformal factor near its infrared stable fixed point.The renormalization group equations for the effective coupling constants are found and their solutions near the critical point are obtained,…
The review presents general methods for treating complicated problems that cannot be solved exactly and whose solution encounters two major difficulties. First, there are no small parameters allowing for the safe use of perturbation theory…
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…
We apply the exact renormalization group formalism to compute the effective action and potential of the four dimensional O$(N)$ linear sigma model in large $N$. With a finite momentum cutoff in place, the model is well defined. In the naive…
The exact renormalization group methods is applied to many fermion systems with short-range attractive force. The strength of the attractive fermion-fermion interaction is determined from the vacuum scattering length. A set of approximate…
We study the functional renormalization group equation and its solutions of the gravity having the background matters. From the system equivalence eliminating vacuum divergence, we are confirmed to give Newton coupling. We also give the…
We study the renormalization group flow of $\mathbb{Z}_2$-invariant supersymmetric and non-supersymmetric scalar models in the local potential approximation using functional renormalization group methods. We focus our attention to the fixed…
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 renormalization group is used to sum the leading-log (LL) contributions to the effective action for a large constant external gauge field in terms of the one-loop renormalization group (RG) function beta, the next-to-leading-log (NLL)…
We construct exact solutions to the functional renormalisation group equation of the O(N) model and the Gross-Neveu model at large N for $2<d<4$, without specifying the form of the regulator. This allows to investigate which quantities are…
The nonperturbative renormalization group has been considered as a solid framework to investigate fixed point and critical exponents for matrix and tensor models, expected to correspond with the so-called double scaling limit. In this…
We apply the functional renormalization group theory to the dynamics of first-order phase transitions and show that a potential with all odd-order terms can describe spinodal decomposition phenomena. We derive a momentum-dependent dynamic…
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…
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…