A Tale of Two Theories: Quantum Griffiths Effects in Metallic Systems

TL;DR

This paper demonstrates the mathematical equivalence of two theories on Griffiths-McCoy singularities in metallic systems, identifying a crossover temperature range where power-law behavior occurs and explaining its suppression at lower temperatures due to dissipation effects.

Contribution

It unifies two conflicting theories on Griffiths effects in metals and characterizes the temperature-dependent crossover behavior with a non-universal scale analogous to the Kondo temperature.

Findings

Power-law Griffiths behavior exists between T* and W.

Below T*, quantum effects are suppressed by dissipation.

T* is controlled by non-universal couplings, similar to Kondo temperature.

Abstract

We show that two apparently contradictory theories on the existence of Griffiths-McCoy singularities in magnetic metallic systems [1,2] are in fact mathematically equivalent. We discuss the generic phase diagram of the problem and show that there is a non-universal crossover temperature range T* < T < W where power law behavior (Griffiths-McCoy behavior) is expect. For T<T* power law behavior ceases to exist due to the destruction of quantum effects generated by the dissipation in the metallic environment. We show that T* is an analogue of the Kondo temperature and is controlled by non-universal couplings.