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.
T. Vojta and J. A. Hoyos, "Criticality and Quenched Disorder: Harris Criterion Versus Rare Regions," Physical Review Letters, vol. 112, no. 7, American Physical Society (APS), Feb 2014.
The definitive version is available at https://doi.org/10.1103/PhysRevLett.112.075702
Center for High Performance Computing Research
Keywords and Phrases
Kinetics; Phase Transition; Quantum Theory; Theoretical Model; Kinetics; Models; Theoretical; Phase Transition; Quantum Theory
International Standard Serial Number (ISSN)
Article - Journal
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