Breakdown of the perturbative renormalization group at certain quantum critical points

D. Belitz; T. R. Kirkpatrick; J. Rollbuehler

doi:10.1103/physrevlett.93.155701

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Breakdown of the perturbative renormalization group at certain quantum critical points

D. Belitz·T. R. Kirkpatrick·J. Rollbuehler

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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.

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D. Belitz, T. R. Kirkpatrick, J. Rollbuehler. 2004-06-16. Breakdown of the perturbative renormalization group at certain quantum critical points. https://doi.org/10.1103/physrevlett.93.155701

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