Dissipation effects in percolating quantum Ising magnets

We study the effects of dissipation on a randomly dilute transverse-field Ising magnet at and close to the percolation threshold. For weak transverse fields, a novel percolation quantum phase transition separates a super-paramagnetic cluster phase from an inhomogeneously ordered ferromagnetic phase. The properties of this transition are dominated by large frozen and slowly fluctuating percolation clusters. Implementing numerically a strong-disorder real space renormalization group technique, we compute the low-energy density of states which is found to be in good agreement with the analytical prediction.Comment: 2 pages, 1 eps figure, final version as publishe

Smeared quantum phase transition in the dissipative random quantum Ising model

We investigate the quantum phase transition in the random transverse-field Ising model under the influence of Ohmic dissipation. To this end, we numerically implement a strong-disorder renormalization-group scheme. We find that Ohmic dissipation destroys the quantum critical point and the associated quantum Griffiths phase by smearing. Our results quantitatively confirm a recent theory [Phys. Rev. Lett. {\bf 100}, 240601 (2008)] of smeared quantum phase transitions.Comment: 7 pages, 10 eps figures embedded, final version as publishe

Criticality and quenched disorder: rare regions vs. Harris criterion

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.Comment: 4.5 pages, 1 eps figure, final version as publishe

Infinite-noise criticality: Nonequilibrium phase transitions in fluctuating environments

We study the effects of time-varying environmental noise on nonequilibrium phase transitions in spreading and growth processes. Using the examples of the logistic evolution equation as well as the contact process, we show that such temporal disorder gives rise to a distinct type of critical points at which the effective noise amplitude diverges on long time scales. This leads to enormous density fluctuations characterized by an infinitely broad probability distribution at criticality. We develop a real-time renormalization-group theory that provides a general framework for the effects of temporal disorder on nonequilibrium processes. We also discuss how general this exotic critical behavior is, we illustrate the results by computer simulations, and we touch upon experimental applications of our theory.Comment: 6 pages (including 3 eps figures). Final version as publishe