Criticality and quenched disorder: rare regions vs. Harris criterion

TL;DR

This paper establishes a theoretical link between quantum Griffiths singularities and the Harris criterion, providing a unified classification of phase transitions in disordered quantum systems based on stability and critical behavior.

Contribution

It introduces a general relation connecting Griffiths singularities and the Harris criterion, offering a unified framework for understanding disordered quantum phase transitions.

Findings

Violating Harris criterion leads to destabilized critical points and diverging Griffiths dynamical exponent.

Fulfilling Harris criterion allows coexistence of Griffiths singularities with stable critical behavior.

The theory applies to quantum spin chains, reaction-diffusion systems, and metallic magnets.

Abstract

We employ scaling arguments and optimal fluctuation theory to establish a general relation between quantum Griffiths singularities and the Harris criterion for quantum phase transitions in disordered systems. If a clean critical point violates the Harris criterion, it is destabilized by weak disorder. At the same time, the Griffiths dynamical exponent $z'$ diverges upon approaching the transition, suggesting unconventional critical behavior. In contrast, if the Harris criterion is fulfilled, power-law Griffiths singularities can coexist with clean critical behavior but $z'$ saturates at a finite value. We present applications of our theory to a variety of systems including quantum spin chains, classical reaction-diffusion systems and metallic magnets; and we discuss modifications for transitions above the upper critical dimension. Based on these results we propose a unified classification of phase transitions in disordered systems.