Preasymptotic Critical Behavior and Effective Exponents in Disordered Metallic Quantum Ferromagnets

We determine the preasymptotic critical behavior at the quantum ferromagnetic transition in strongly disordered metals. We find that it is given by effective power laws, in contrast to the previously analyzed asymptotic critical behavior, which is valid only in an unobservably small region. The consequences for analyzing experiments are discussed, in particular, ways to distinguish between critical behavior and Griffiths-phase effects.

Figure 1

Solution of Eqs. (7). Main frame: $D(\mathrm{\Omega }=0)/D^0$ as a function of $t$. Inset: log-log plot of the same data. The straight line corresponds to a slope $\kappa =0.4$.

Figure 2

$D(\mathrm{\Omega })$ (blue dots) and $D_{\mathrm{s}}(0,\mathrm{\Omega })$ (green diamonds) at criticality. $\mathrm{\Omega }$, $D$, and $D_{\mathrm{s}}$ are measured in atomic units as in Ref. [23]. Inset: log-log plot of the same data; the straight lines correspond to ${\kappa }_T=0.181$ and ${\gamma }_T=0.625$.