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 …

We study the optimization of exact renormalization group (ERG) flows. We explain why the
convergence of approximate solutions towards the physical theory is optimized by …

A microscopic calculation of ground state entanglement for the XY and Heisenberg models
shows the emergence of universal scaling behavior at quantum phase transitions …

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 review and extend in several directions recent results on the “asymptotic safety”
approach to quantum gravity. The central issue in this approach is the search of a Fixed …

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 …

This article reviews recent advances in the theory of the three-dimensional dilute
homogeneous Bose gas at zero and finite temperature. Effective-field-theory methods are …