On exactly solvable models for systems with quantum-phase transitions

A reduction procedure, suggested for classical systems some years ago, is extended to systems with quantum-phase transitions with the aim to generate exactly solvable models capturing fluctuation effects beyond the mean field approximation. For the reduced isotropic m-vector quantum models, an exact nonperturbative renormalization group formulation is presented and the relation to the classical counterpart is established. We show that, with a simple change of the coupling functional, it is possible to reproduce formally the flow differential equations already obtained in the large-m limit many years ago. The substantial difference is that the reduction procedure used here does not impose any restriction on the dimension m of the order parameter field.