Breakdown of the perturbative renormalization group at certain quantum critical points

Abstract

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 be not be an approximation in any sense to the true asymptotic critical behavior. This problem manifests itself as a non-renormalizable field theory, or, equivalently, as the presence of a dangerous irrelevant variable. The quantum ferromagnetic transition in disordered metals provides an example.

arXiv comment4pp, 1 eps fig

References in corpus (4)

• Quantum critical behavior of disordered itinerant ferromagnets
• Local field theory for disordered itinerant quantum ferromagnets
• Nature of the Quantum Phase Transition in Clean, Itinerant Heisenberg Ferromagnets
• Quantum critical behavior in disordered itinerant ferromagnets: Logarithmic corrections to scaling

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• Orbital currents and charge density waves in a generalized Hubbard ladder
• Instability of the ferromagnetic quantum critical point in strongly interacting 2D and 3D electron gases with arbitrary spin-orbit splitting
• Quantum Metal--Superconductor Transition: A Local Field Theory Approach