The motivation and the challenge in applying the renormalization group for systems with several scaling regimes is briefly outlined. The four dimensional φ4 model serves as an example where a nontrivial low energy scaling regime is identified in the vicinity of the spinodal instability region. It is pointed out that the effective theory defined in the vicinity of the spinodal instability offers...

We present a variational renormalization group approach using deep generative model composed of bijectors. The model can learn hierarchical transformations between physical variables and renormalized collective variables. It can directly generate statistically independent physical configurations by iterative refinement at various length scales. The generative model has an exact and tractable li...

Quantum field theories require a cutoff to regulate divergences that result from local interactions, and yet physical results can not depend on the value of this cutoff. The renormalization group employs a transformation that changes the cutoff to isolate hamiltonians that produce cutoff-independent eigenvalues. The similarity renormalization group is based on similarity transformations that re...

The holographic renormalization group (RG) is reviewed in a self-contained manner. The holographic RG is based on the idea that the radial coordinate of a space-time with asymptotically AdS geometry can be identified with the RG flow parameter of the boundary field theory. After briefly discussing basic aspects of the AdS/CFT correspondence, we explain how the notion of the holographic RG comes...

Functional renormalization group (FRG) has become a diverse and powerful tool to derive effective low-energy scattering vertices of interacting many-body systems. Starting from a non-interacting expansion point of the action, the flow of the RG parameter Λ allows to trace the evolution of the effective one-particle and two-particle vertices towards low energies by taking into account the vertex...