  The pseudogap Kondo problem, describing a magnetic impurity embedded in an
electronic environment with a power-law density of states, displays continuous
quantum phase transitions between free and screened moment phases. In this
paper we employ renormalization group techniques to analytically calculate
universal crossover functions, associated to these transitions, for various
observables. Quantitative agreement with the results of Numerical
Renormalization Group (NRG) simulations is obtained for temperature-dependent
static and zero-temperature dynamic quantities, at and away from criticality.
In the notoriously difficult realm of finite-temperature low-frequency
dynamics, usually inaccessible to both NRG and perturbative methods, we show
that progress can be made by a suitable renormalization procedure in the
framework of the Callan-Symanzik equations. Our general strategy can be
extended to other zero-temperature phase transitions, both in quantum impurity
models and bulk systems.
