Quantum critical scenario from an effective classical renormalization group treatment close to and below four dimensions

We suggest a general procedure to analyze quantum criticality for a wide variety of quantum systems of topical interest, close and below four dimensions. The idea is to apply the Wilsonian renormalization group philosophy to an effective classical functional derived from a general quantum action by averaging over degrees of freedom with non-zero Matsubara frequencies. This allows us to describe, in an unified way, all crossovers expected close to a quantum critical point.