Temperature-dependent scaling fields and quantum criticality within the Wilson renormalization group approach

Abstract

Within the Wilson Renormalization Group (WRG) approach as applied to d-dimensional quantum systems using appropriate functional representations, we develop a general method for describing the critical behaviour driven by the temperature T when the quantum fluctuations are into play. It consists in solving the quantum RG equations near a zero-temperature fixed point (FP) introducing T-dependent scaling fields which are determined by ordinary first-order differential equations with appropriate boundary conditions. This allows us to explore, in a unified and relatively simple way, the low-temperature properties near a ( T = 0)-quantum instability of a great variety of quantum systems (interacting Bose gas, quantum ferroelectrics, itinerant fermion materials, spin models in a tranverse field, granular superconductors, etc.). The crossover from the low-but finite-temperature critical behaviour to the quantum criticality is also described in a natural way in terms of appropriate effective exponents. The predictions appear to be quite quantum systems by means of different approaches. For the interacting Bose gas and other quantum systems lying in the same universality class (bosonic systems), our results give us the opportunity to rexamine some uncorrect calculations for d ≤2 recently appeared in the literature.