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 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 …

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 …

We discuss structural aspects of the functional renormalisation group. Flows for a general
class of correlation functions are derived, and it is shown how symmetry relations of the …

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 …

The asymptotic safety conjecture is examined for quantum gravity in four dimensions. Using
the renormalization group, we find evidence for an interacting UV fixed point for polynomial …

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 …

Within the exact renormalisation group, the scaling solutions for O (N) symmetric scalar field
theories are studied to leading order in the derivative expansion. The Gaussian fixed point is …

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 …

On the example of the three-dimensional Ising model, we show that nonperturbative
renormalization group equations allow one to obtain very accurate critical exponents …