488 research outputs found
Theory of the critical state of low-dimensional spin glass
We analyse the critical region of finite-()-dimensional Ising spin glass,
in particular the limit of closely above the lower critical dimension
. At criticality the thermally active degrees of freedom are surfaces
(of width zero) enclosing clusters of spins that may reverse with respect to
their environment. The surfaces are organised in finite interacting structures.
These may be called {\em protodroplets}\/, since in the off-critical limit they
reduce to the Fisher and Huse droplets. This picture provides an explanation
for the phenomenon of critical chaos discovered earlier. It also implies that
the spin-spin and energy-energy correlation functions are multifractal and we
present scaling laws that describe them. Several of our results should be
verifiable in Monte Carlo studies at finite temperature in .Comment: RevTeX, 33 pages + 1 PostScript figure (uuencoded). Uses german.sty
and an input file def.tex, joined. Three additional figures may be requested
from the author
Chaos in a Two-Dimensional Ising Spin Glass
We study chaos in a two dimensional Ising spin glass by finite temperature
Monte Carlo simulations. We are able to detect chaos with respect to
temperature changes as well as chaos with respect to changing the bonds, and
find that the chaos exponents for these two cases are equal. Our value for the
exponent appears to be consistent with that obtained in studies at zero
temperature.Comment: 4 pages, LaTeX, 4 postscript figures included. The analysis of the
data is now done somewhat differently. The results are consistent with the
chaos exponent found at zero temperature. Additional papers of PY can be
obtained on-line at http://schubert.ucsc.edu/pete
Numerical Study of Spin and Chiral Order in a Two-Dimensional XY Spin Glass
The two dimensional XY spin glass is studied numerically by a finite size
scaling method at T=0 in the vortex representation which allows us to compute
the exact (in principle) spin and chiral domain wall energies. We confirm
earlier predictions that there is no glass phase at any finite T. Our results
strongly support the conjecture that both spin and chiral order have the same
correlation length exponent . We obtain preliminary results
in 3d.Comment: 4 pages, 2 figures, revte
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
Numerical Study of Order in a Gauge Glass Model
The XY model with quenched random phase shifts is studied by a T=0 finite
size defect energy scaling method in 2d and 3d. The defect energy is defined by
a change in the boundary conditions from those compatible with the true ground
state configuration for a given realization of disorder. A numerical technique,
which is exact in principle, is used to evaluate this energy and to estimate
the stiffness exponent . This method gives in
2d and in 3d, which are considerably larger than
previous estimates, strongly suggesting that the lower critical dimension is
less than three. Some arguments in favor of these new estimates are given.Comment: 4 pages, 2 figures, revtex. Submitted to Phys. Rev. Let
Griffiths-McCoy singularities in the transverse field Ising model on the randomly diluted square lattice
The site-diluted transverse field Ising model in two dimensions is studied
with Quantum-Monte-Carlo simulations. Its phase diagram is determined in the
transverse field (Gamma) and temperature (T) plane for various (fixed)
concentrations (p). The nature of the quantum Griffiths phase at zero
temperature is investigated by calculating the distribution of the local
zero-frequency susceptibility. It is pointed out that the nature of the
Griffiths phase is different for small and large Gamma.Comment: 21 LaTeX (JPSJ macros included), 12 eps-figures include
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
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
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