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 derive a new exact evolution equation for the scale dependence of an effective action.
The corresponding equation for the effective potential permits a useful truncation. This …

We investigate the structure of Polchinski's formulation of the flow equations for the
continuum Wilson effective action. Reinterpretations in terms of IR cutoff Green's functions …

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 …

In this paper, we present an overview on recent progress in studies of QCD at finite
temperature and densities within the functional renormalization group (fRG) approach. The …

Numerous correlated electron systems exhibit a strongly scale-dependent behavior. Upon
lowering the energy scale, collective phenomena, bound states, and new effective degrees …

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 …

Recently the series for two renormalization group functions (corresponding to the
anomalous dimensions of the fields and) of the three-dimensional field theory have been …