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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…
We report on particle physics applications of the renormalization group equation of Newton's constant.
Over the last several years, there has been a resurgence of interest in using non-perturbative approximation methods based on Wilson's continuous renormalization group. In this lecture, I review progress particularly in the past year,…
We provide rates of convergence in the central limit theorem in terms of projective criteria for adapted stationary sequences of centered random variables taking values in Banach spaces, with finite moment of order $p \in ]2,3]$ as soon as…
Using the renormalization group method, we improved the first order solution of the long-wavelength expansion of the Einstein equation. By assuming that the renormalization group transformation has the property of Lie group, we can…
The critical behavior of a quenched random hypercubic sample of linear size $L$ is considered, within the ``random-$T_{c}$'' field-theoretical mode, by using the renormalization group method. A finite-size scaling behavior is established…
The Kadanoff-Wilson renormalization group approach for a scalar self-interacting field theor generally coupled with gravity is presented. An average potential that monitors the fluctuations of the blocked field in different scaling regimes…
We construct a general renormalization group transformation on quantum states, independent of any Hamiltonian dynamics of the system. We illustrate this procedure for translational invariant matrix product states in one dimension and show…
Nonrelativistic two-body scattering by a short-ranged potential is studied using the renormalisation group. Two fixed points are identified: a trivial one and one describing systems with a bound state at zero energy. The eigenvalues of the…
A Wilsonian renormalisation group is used to study nonrelativistic two-body scattering by a short-ranged potential. We identify two fixed points: a trivial one and one describing systems with a bound state at zero energy. The eigenvalues of…
The renormalization group (RG) approach is largely responsible for the considerable success that has been achieved in developing a quantitative theory of phase transitions. Physical properties emerge from spectral properties of the…
The infinite disorder fixed point of the random transverse-field Ising model is expected to control the critical behavior of a large class of random quantum and stochastic systems having an order parameter with discrete symmetry. Here we…
In a system of noisy self-propelled particles with interactions that favor directional alignment, collective motion will appear if the density of particles is beyond a critical density. Starting with a reduced model for collective motion,…
We propose a new Real Space Renormalization Group transformation useful for Monte Carlo calculations in theories with global or local symmetries. From relaxation arguments we define the block-spin transformation with two tunable free…
The paper examines questions of local asymptotic stability of random dynamical systems. Results concerning stochastic dynamics in general metric spaces, as well as in Banach spaces, are obtained. The results pertaining to Banach spaces are…
Similarity renormalization group procedure identifies the role of bound states in the low-energy rate of change of effective coupling constant in a model Hamiltonian with asymptotic freedom.
We develop a scaling theory and a renormalization technique in the context of the modern theory of polarization. The central idea is to use the characteristic function (also known as the polarization amplitude) in place of the free energy…
The renormalization group method is a successive integration over the fluctuations which are ordered according to their length scale, a parameter in the external space. A different procedure is described, where the fluctuations are treated…
The renormalization group approach towards the string representation of non abelian gauge theories translates, in terms of the string sigma model beta function equations, the renormalization group evolution of the gauge coupling constant…
Renormalization group theory is a powerful and intriguing technique with a wide range of applications. One of the main successes of renormalization group theory is the description of continuous phase transitions and the development of…