The Wilson–Polchinski exact renormalization group equation

  title={The Wilson–Polchinski exact renormalization group equation},
  author={C. Bervillier},
  journal={Physics Letters A},

Wilson–Polchinski exact renormalization group equation for O (N) systems: leading and next-to-leading orders in the derivative expansion

With a view to study the convergence properties of the derivative expansion of the exact renormalization group (RG) equation, I explicitly study the leading and next-to-leading orders of this

Remarks on exact RG equations

Nonlinear aspects of the renormalization group flows of Dyson's hierarchical model

We review recent results concerning the renormalization group (RG) transformation of Dyson's hierarchical model (HM). This model can be seen as an approximation of a scalar field theory on a lattice.

Universality and the renormalisation group

Several functional renormalisation group (RG) equations including Polchinski flows and Exact RG flows are compared from a conceptual point of view and in given truncations. Similarities and

Reparameterization invariance and RG equations: extension of the local potential approximation

Equations related to the Polchinski version of the exact renormalization group (RG) equations for scalar fields which extend the local potential approximation to first order in a derivative

Integrability properties of renormalization group flow

We consider the Polchinski RG equation for a theory of matrix scalar fields interacting with single trace operators and show that it can be written in a Hamiltonian form for a specific choice of the

Optimization of field-dependent nonperturbative renormalization group flows

We investigate the influence of the momentum cutoff function on the field-dependent nonperturbative renormalization group flows for the three-dimensional Ising model, up to the second order of the

The fate of non-polynomial interactions in scalar field theory

We present an exact RG (renormalization group) analysis of O(N)-invariant scalar field theory about the Gaussian fixed point. We prove a series of statements that taken together show that the

Equivalence of local potential approximations

In recent papers it has been noted that the local potential approximation of the Legendre and Wilson-Polchinski flow equations give, within numerical error, identical results for a range of exponents



The renormalization group: Critical phenomena and the Kondo problem

This review covers several topics involving renormalization group ideas. The solution of the $s$-wave Kondo Hamiltonian, describing a single magnetic impurity in a nonmagnetic metal, is explained in

Optimization of the derivative expansion in the nonperturbative renormalization group

We study the optimization of nonperturbative renormalization group equations truncated both in fields and derivatives. On the example of the Ising model in three dimensions, we show that the

Fast-convergent resummation algorithm and critical exponents of φ4-theory in three dimensions

We develop an efficient algorithm for evaluating divergent perturbation expansions of field theories in the bare coupling constant gB for which we possess a finite number L of expansion coefficients