Breakdown of the perturbative renormalization group at certain quantum critical points.
It is shown that the presence of multiple time scales at a quantum critical point can lead to a breakdown of the loop expansion for critical exponents, since coefficients in the expansion diverge. Consequently, results obtained from finite-order perturbative renormalization-group treatments may not be an approximation in any sense to the true asymptotic critical behavior. This problem manifests itself as a nonrenormalizable field theory, or, equivalently, as the presence of a dangerous irrelevant variable. The quantum ferromagnetic transition in disordered metals provides an example.
Belitz
D
D
Department of Physics and Materials Science Institute, University of Oregon, Eugene, Oregon 97403, USA.
Kirkpatrick
T R
TR
Rollbühler
Jörg
J