Breakdown of the perturbative renormalization group at certain quantum critical points

Details Breakdown of the perturbative renormalization group at certain quantum critical points Breakdown of the perturbative renormalization group at certain quantum critical points

2004-06-16

arxiv.org/abs/cond-mat/0406350v1

Phys.Rev.Lett. 93 (2004) 155701

Physics

Condensed Matter

Statistical Mechanics

4pp, 1 eps fig

Scientific paper

10.1103/PhysRevLett.93.155701

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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