Pre-asymptotic critical behavior and effective exponents in disordered metallic quantum ferromagnets

TL;DR

This paper investigates the pre-asymptotic critical behavior in disordered metallic quantum ferromagnets, revealing effective power laws that differ from the asymptotic behavior, with implications for experimental analysis.

Contribution

It introduces the concept of effective power laws governing pre-asymptotic critical behavior in disordered quantum ferromagnets, contrasting with the traditional asymptotic analysis.

Findings

Pre-asymptotic behavior follows effective power laws.

Asymptotic critical behavior is only observable in an extremely small region.

Guidelines for experimental distinction between critical and Griffiths-phase effects.

Abstract

We determine the pre-asymptotic 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.