Generalized coarse-graining applied to a phi 4-theory: A model reduction-renormalization group synthesis

Abstract

We develop an algorithmic, system-specific renormalization group (RG) procedure that is adapted from model reductions techniques from engineering control theory. The resulting "generalized" RG is a consistent generalization of the Wilsonian RG. We apply the generalized RG to a phi 4-field theory. By considering nonequilibrium in addition to equilibrium observables, we find that naive power counting break down. Additionally, a large class of short-wavelength perturbations can drive the system away from both the Gaussian and Wilson-Fisher fixed points.