Reply to Millis et al. on "A Tale of Two Theories: Quantum Griffiths Effects in Metallic Systems"

TL;DR

This paper defends the authors' previous theory on Griffiths-McCoy singularities in metallic antiferromagnets near quantum critical points, arguing that a self-consistent approach shows weak damping and extensive Griffiths behavior contrary to recent criticisms.

Contribution

It clarifies the theoretical understanding of Griffiths-McCoy singularities by emphasizing the importance of self-consistent treatment of disorder near quantum critical points.

Findings

Self-consistent treatment leads to weak damping in metallic systems.

Large Griffiths-McCoy singularities are possible near QCPs.

Critique based on non-self-consistent analysis is incorrect.

Abstract

In a recent paper (cond-mat/0411197) we showed the equivalence of two seemingly contradictory theories on Griffiths-McCoy singularities (GMS) in metallic antiferromagnets close to a quantum critical point (QCP). In a recent comment, Millis {\it et al.} (cond-mat/0411738) argue that in heavy-fermion materials the electronic damping is large leading to the freezing of locally magnetically ordered droplets at high temperatures. In this reply we show that this erroneous conclusion is based on a treatment of the problem of disorder close to a QCP which is not self-consistent. We argue that a self-consistent treatment of the ordered droplets must lead to weak damping and to a large region of GMS behavior, in agreement with the our ealier results.