284 research outputs found
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 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 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
Local defect in a magnet with long-range interactions
We investigate a single defect coupling to the square of the order parameter
in a nearly critical magnet with long-range spatial interactions of the form
, focusing on magnetic droplets nucleated at the defect while
the bulk system is in the paramagnetic phase. Because of the long-range
interaction, the droplet develops a power-law tail which is energetically
unfavorable. However, as long as , the tail contribution to the
droplet free energy is subleading in the limit of large droplets; and the free
energy becomes identical to the case of short-range interactions. We also study
the droplet quantum dynamics with and without dissipation; and we discuss the
consequences of our results for defects in itinerant quantum ferromagnets.Comment: 8 pages, 5 eps figures, final version, as publishe
Rounding of a first-order quantum phase transition to a strong-coupling critical point
We investigate the effects of quenched disorder on first-order quantum phase
transitions on the example of the -color quantum Ashkin-Teller model. By
means of a strong-disorder renormalization group, we demonstrate that quenched
disorder rounds the first-order quantum phase transition to a continuous one
for both weak and strong coupling between the colors. In the strong coupling
case, we find a distinct type of infinite-randomness critical point
characterized by additional internal degrees of freedom. We investigate its
critical properties in detail, and we discuss broader implications for the fate
of first-order quantum phase transitions in disordered systems.Comment: 5 pages, 4 figure
Rare regions and Griffiths singularities at a clean critical point: The five-dimensional disordered contact process
We investigate the nonequilibrium phase transition of the disordered contact
process in five space dimensions by means of optimal fluctuation theory and
Monte Carlo simulations. We find that the critical behavior is of mean-field
type, i.e., identical to that of the clean five-dimensional contact process. It
is accompanied by off-critical power-law Griffiths singularities whose
dynamical exponent saturates at a finite value as the transition is
approached. These findings resolve the apparent contradiction between the
Harris criterion which implies that weak disorder is renormalization-group
irrelevant and the rare-region classification which predicts unconventional
behavior. We confirm and illustrate our theory by large-scale Monte-Carlo
simulations of systems with up to sites. We also relate our results to a
recently established general relation between the Harris criterion and
Griffiths singularities [Phys. Rev. Lett. {\bf 112}, 075702 (2014)], and we
discuss implications for other phase transitions.Comment: 10 pages, 5 eps figures included, applies the optimal fluctuation
theory of arXiv:1309.0753 to the contact proces
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
Emergent SU(3) symmetry in random spin-1 chains
We show that generic SU(2)-invariant random spin-1 chains have phases with an
emergent SU(3) symmetry. We map out the full zero-temperature phase diagram and
identify two different phases: (i) a conventional random singlet phase (RSP) of
strongly bound spin pairs (SU(3) "mesons") and (ii) an unconventional RSP of
bound SU(3) "baryons", which are formed, in the great majority, by spin trios
located at random positions. The emergent SU(3) symmetry dictates that
susceptibilities and correlation functions of both dipolar and quadrupolar spin
operators have the same asymptotic behavior.Comment: 5 pages plus 3-page Supplemental Material, 5 figures; published
versio
Dissipation effects in random transverse-field Ising chains
We study the effects of Ohmic, super-Ohmic, and sub-Ohmic dissipation on the
zero-temperature quantum phase transition in the random transverse-field Ising
chain by means of an (asymptotically exact) analytical strong-disorder
renormalization-group approach. We find that Ohmic damping destabilizes the
infinite-randomness critical point and the associated quantum Griffiths
singularities of the dissipationless system. The quantum dynamics of large
magnetic clusters freezes completely which destroys the sharp phase transition
by smearing. The effects of sub-Ohmic dissipation are similar and also lead to
a smeared transition. In contrast, super-Ohmic damping is an irrelevant
perturbation; the critical behavior is thus identical to that of the
dissipationless system. We discuss the resulting phase diagrams, the behavior
of various observables, and the implications to higher dimensions and
experiments.Comment: 18 pages, 3 figures; (v2) minor changes, published versio
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