The renormalization group plays an essential role in many areas of physics, both
conceptually and as a practical tool to determine the long-distance low-energy properties of …

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→ 0 …

We review the use of an exact renormalization group equation in quantum field theory and
statistical physics. It describes the dependence of the free energy on an infrared cutoff for the …

A scale-dependent effective action for gravity is introduced and an exact nonperturbative
evolution equation is derived which governs its renormalization group flow. It is invariant …

Various aspects of the Exact Renormalization Group (ERG) are explored, starting with a
review of the concepts underpinning the framework and the circumstances under which it is …

We give in these notes a short presentation of both the main ideas underlying Wilson's
renormalization group (RG) and their concrete implementation under the form of what is now …

We critically review the use of the exact renormalization group equations (ERGE) in the
framework of the scalar theory. We lay emphasis on the existence of different versions of the …

These introductory notes are about functional renormalization group equations and some of
their applications. It is emphasised that the applicability of this method extends well beyond …

A bstract In the asymptotic safety programme for quantum gravity, it is important to go
beyond polynomial truncations. Three such approximations have been derived where the …

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 …