title: Criticality and quenched disorder: Harris criterion versus rare regions.
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.
authors.affiliation: Department of Physics, Missouri University of Science and Technology, Rolla, Missouri 65409, USA.
authors.forename: Thomas
authors.initials: T
authors.lastname: Vojta
authors.affiliation: Instituto de Física de São Carlos, Universidade de São Paulo, C.P. 369, São Carlos, São Paulo 13560-970, Brazil.
authors.forename: José A
authors.initials: JA
authors.lastname: Hoyos
mesh_terms: D007700:Kinetics; D008962:Models, Theoretical; D044367:Phase Transition; D011789:Quantum Theory