326 research outputs found
Finite Temperature and Dynamical Properties of the Random Transverse-Field Ising Spin Chain
We study numerically the paramagnetic phase of the spin-1/2 random
transverse-field Ising chain, using a mapping to non-interacting fermions. We
extend our earlier work, Phys. Rev. 53, 8486 (1996), to finite temperatures and
to dynamical properties. Our results are consistent with the idea that there
are ``Griffiths-McCoy'' singularities in the paramagnetic phase described by a
continuously varying exponent , where measures the
deviation from criticality. There are some discrepancies between the values of
obtained from different quantities, but this may be due to
corrections to scaling. The average on-site time dependent correlation function
decays with a power law in the paramagnetic phase, namely
, where is imaginary time. However, the typical
value decays with a stretched exponential behavior, ,
where may be related to . We also obtain results for the full
probability distribution of time dependent correlation functions at different
points in the paramagnetic phase.Comment: 10 pages, 14 postscript files included. The discussion of the typical
time dependent correlation function has been greatly expanded. Other papers
of APY are available on-line at http://schubert.ucsc.edu/pete
Short-Range Ising Spin Glass: Multifractal Properties
The multifractal properties of the Edwards-Anderson order parameter of the
short-range Ising spin glass model on d=3 diamond hierarchical lattices is
studied via an exact recursion procedure. The profiles of the local order
parameter are calculated and analysed within a range of temperatures close to
the critical point with four symmetric distributions of the coupling constants
(Gaussian, Bimodal, Uniform and Exponential). Unlike the pure case, the
multifractal analysis of these profiles reveals that a large spectrum of the
-H\"older exponent is required to describe the singularities of the
measure defined by the normalized local order parameter, at and below the
critical point. Minor changes in these spectra are observed for distinct
initial distributions of coupling constants, suggesting an universal spectra
behavior. For temperatures slightly above T_{c}, a dramatic change in the
function is found, signalizing the transition.Comment: 8 pages, LaTex, PostScript-figures included but also available upon
request. To be published in Physical Review E (01/March 97
Quantum Spin Glasses
Ising spin glasses in a transverse field exhibit a zero temperature quantum
phase transition, which is driven by quantum rather than thermal fluctuations.
They constitute a universality class that is significantly different from the
classical, thermal phase transitions. Most interestingly close to the
transition in finite dimensions a quantum Griffiths phase leads to drastic
consequences for various physical quantities: for instance diverging magnetic
susceptibilities are observable over a whole range of transverse field values
in the disordered phase.Comment: 10 pages LaTeX (Springer Lecture Notes style file included), 1
eps-figure; Review article for XIV Sitges Conference: Complex Behavior of
Glassy System
Properties of the random field Ising model in a transverse magnetic field
We consider the effect of a random longitudinal field on the Ising model in a
transverse magnetic field. For spatial dimension , there is at low
strength of randomness and transverse field, a phase with true long range order
which is destroyed at higher values of the randomness or transverse field. The
properties of the quantum phase transition at zero temperature are controlled
by a fixed point with no quantum fluctuations. This fixed point also controls
the classical finite temperature phase transition in this model. Many critical
properties of the quantum transition are therefore identical to those of the
classical transition. In particular, we argue that the dynamical scaling is
activated, i.e, the logarithm of the diverging time scale rises as a power of
the diverging length scale
Domain Wall Renormalization Group Study of XY Model with Quenched Random Phase Shifts
The XY model with quenched random disorder is studied by a zero temperature
domain wall renormalization group method in 2D and 3D. Instead of the usual
phase representation we use the charge (vortex) representation to compute the
domain wall, or defect, energy. For the gauge glass corresponding to the
maximum disorder we reconfirm earlier predictions that there is no ordered
phase in 2D but an ordered phase can exist in 3D at low temperature. However,
our simulations yield spin stiffness exponents in 2D
and in 3D, which are considerably larger than
previous estimates and strongly suggest that the lower critical dimension is
less than three. For the XY spin glass in 3D, we obtain a spin
stiffness exponent which supports the existence of
spin glass order at finite temperature in contrast with previous estimates
which obtain . Our method also allows us to study
renormalization group flows of both the coupling constant and the disorder
strength with length scale . Our results are consistent with recent analytic
and numerical studies suggesting the absence of a re-entrant transition in 2D
at low temperature. Some possible consequences and connections with real vortex
systems are discussed.Comment: 14 pages, 9 figures, revtex
Random quantum magnets with long-range correlated disorder: Enhancement of critical and Griffiths-McCoy singularities
We study the effect of spatial correlations in the quenched disorder on
random quantum magnets at and near a quantum critical point. In the random
transverse field Ising systems disorder correlations that decay algebraically
with an exponent rho change the universality class of the transition for small
enough rho and the off-critical Griffiths-McCoy singularities are enhanced. We
present exact results for 1d utilizing a mapping to fractional Brownian motion
and generalize the predictions for the critical exponents and the generalized
dynamical exponent in the Griffiths phase to d>=2.Comment: 4 pages RevTeX, 1 eps-figure include
Griffiths-McCoy Singularities in the Random Transverse-Field Ising Spin Chain
We consider the paramagnetic phase of the random transverse-field Ising spin
chain and study the dynamical properties by numerical methods and scaling
considerations. We extend our previous work [Phys. Rev. B 57, 11404 (1998)] to
new quantities, such as the non-linear susceptibility, higher excitations and
the energy-density autocorrelation function. We show that in the Griffiths
phase all the above quantities exhibit power-law singularities and the
corresponding critical exponents, which vary with the distance from the
critical point, can be related to the dynamical exponent z, the latter being
the positive root of [(J/h)^{1/z}]_av=1. Particularly, whereas the average spin
autocorrelation function in imaginary time decays as [G]_av(t)~t^{-1/z}, the
average energy-density autocorrelations decay with another exponent as
[G^e]_av(t)~t^{-2-1/z}.Comment: 8 pages RevTeX, 8 eps-figures include
The metastate approach to thermodynamic chaos
In realistic disordered systems, such as the Edwards-Anderson (EA) spin
glass, no order parameter, such as the Parisi overlap distribution, can be both
translation-invariant and non-self-averaging. The standard mean-field picture
of the EA spin glass phase can therefore not be valid in any dimension and at
any temperature. Further analysis shows that, in general, when systems have
many competing (pure) thermodynamic states, a single state which is a mixture
of many of them (as in the standard mean-field picture) contains insufficient
information to reveal the full thermodynamic structure. We propose a different
approach, in which an appropriate thermodynamic description of such a system is
instead based on a metastate, which is an ensemble of (possibly mixed)
thermodynamic states. This approach, modelled on chaotic dynamical systems, is
needed when chaotic size dependence (of finite volume correlations) is present.
Here replicas arise in a natural way, when a metastate is specified by its
(meta)correlations. The metastate approach explains, connects, and unifies such
concepts as replica symmetry breaking, chaotic size dependence and replica
non-independence. Furthermore, it replaces the older idea of non-self-averaging
as dependence on the bulk couplings with the concept of dependence on the state
within the metastate at fixed coupling realization. We use these ideas to
classify possible metastates for the EA model, and discuss two scenarios
introduced by us earlier --- a nonstandard mean-field picture and a picture
intermediate between that and the usual scaling/droplet picture.Comment: LaTeX file, 49 page
Non-Fermi liquid behavior and Griffiths phase in {\it f}-electron compounds
We study the interplay among disorder, RKKY and Kondo interactions in {\it
f}-electron alloys. We argue that the non-Fermi liquid behavior observed in
these systems is due to the existence of a Griffiths phase close to a quantum
critical point. The existence of this phase provides a unified picture of a
large class of materials. We also propose new experiments that can test these
ideas.Comment: 4 pages, 1 Figure. NEW version of the original manuscript. A single
framework for NFL behavior in different kinds of alloys is presented. Final
version finally allowed to appear on the glorious Physical Review Letter
Organizational and Supervisory Apology Effectiveness: Apology Giving in Work Settings
We synthesize the interdisciplinary literature into a heuristic for crafting effective organizational and supervisory apologies (the OOPS four-component apology). In the first experiment, we demonstrate how an offense committed by an organization is perceived to be more egregious than an offense committed by a friend or supervisor. Furthermore, results did not support that OOPS apologies are unequally effective if issued by a friend, supervisor, or organization. In the second experiment, we test OOPS apology-training effectiveness. Results indicated that trained participants crafted more effective apologies. Our apology heuristic is an innovation for training business communicators how to apologize effectively.Yeshttps://us.sagepub.com/en-us/nam/manuscript-submission-guideline
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