855 research outputs found
Ordered droplets in quantum magnets with long-range interactions
A defect coupling to the square of the order parameter in a nearly
quantum-critical magnet can nucleate an ordered droplet while the bulk system
is in the paramagnetic phase. We study the influence of long-range spatial
interactions of the form on the droplet formation. To this
end, we solve a Landau-Ginzburg-Wilson free energy in saddle point
approximation. The long-range interaction causes the droplet to develop an
energetically unfavorable power-law tail. However, for , the free
energy contribution of this tail is subleading in the limit of large droplets;
and the droplet formation is controlled by the defect bulk. Thus, for large
defects, long-range interactions do not hinder the formation of droplets.Comment: 2 pages, 3 eps figures, 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
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
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
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
Upper-critical dimension in a quantum impurity model: Critical theory of the asymmetric pseudogap Kondo problem
Impurity moments coupled to fermions with a pseudogap density of states
display a quantum phase transition between a screened and a free moment phase
upon variation of the Kondo coupling. We describe the universal theory of this
transition for the experimentally relevant case of particle-hole asymmetry. The
theory takes the form of a crossing between effective singlet and doublet
levels, interacting with low-energy fermions. Depending on the pseudogap
exponent, this interaction is either relevant or irrelevant under
renormalization group transformations, establishing the existence of an
upper-critical "dimension" in this impurity problem. Using perturbative
renormalization group techniques we compute various critical properties and
compare with numerical results.Comment: 4 pages, 2 figs, (v2) title changed, log corrections for r=1 adde
Percolation transition in quantum Ising and rotor models with sub-Ohmic dissipation
We investigate the influence of sub-Ohmic dissipation on randomly diluted
quantum Ising and rotor models. The dissipation causes the quantum dynamics of
sufficiently large percolation clusters to freeze completely. As a result, the
zero-temperature quantum phase transition across the lattice percolation
threshold separates an unusual super-paramagnetic cluster phase from an
inhomogeneous ferromagnetic phase. We determine the low-temperature
thermodynamic behavior in both phases which is dominated by large frozen and
slowly fluctuating percolation clusters. We relate our results to the smeared
transition scenario for disordered quantum phase transitions, and we compare
the cases of sub-Ohmic, Ohmic, and super-Ohmic dissipation.Comment: 9 pages, 2 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
Breakdown of Landau-Ginzburg-Wilson theory for certain quantum phase transitions
The quantum ferromagnetic transition of itinerant electrons is considered. It
is shown that the Landau-Ginzburg-Wilson theory described by Hertz and others
breaks down due to a singular coupling between fluctuations of the conserved
order parameter. This coupling induces an effective long-range interaction
between the spins of the form 1/r^{2d-1}. It leads to unusual scaling behavior
at the quantum critical point in dimensions, which is determined
exactly.Comment: 4 pp., REVTeX, no figs, 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
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