45 research outputs found
Chaos in Glassy Systems from a TAP Perspective
We discuss level crossing of the free-energy of TAP solutions under
variations of external parameters such as magnetic field or temperature in
mean-field spin-glass models that exhibit one-step Replica-Symmetry-Breaking
(1RSB). We study the problem through a generalized complexity that describes
the density of TAP solutions at a given value of the free-energy and a given
value of the extensive quantity conjugate to the external parameter. We show
that variations of the external parameter by any finite amount can induce level
crossing between groups of TAP states whose free-energies are extensively
different. In models with 1RSB, this means strong chaos with respect to the
perturbation. The linear-response induced by extensive level crossing is
self-averaging and its value matches precisely with the disorder-average of the
non self-averaging anomaly computed from the 2nd moment of thermal fluctuations
between low-lying, almost degenerate TAP states. We present an analytical
recipe to compute the generalized complexity and test the scenario on the
spherical multi- spin models under variation of temperature.Comment: 12 pages, 2 figure
Chaos and Universality in a Four-Dimensional Spin Glass
We present a finite size scaling analysis of Monte Carlo simulation results
on a four dimensional Ising spin glass. We study chaos with both coupling and
temperature perturbations, and find the same chaos exponent in each case. Chaos
is investigated both at the critical temperature and below where it seems to be
more efficient (larger exponent). Dimension four seems to be above the critical
dimension where chaos with temperature is no more present in the critical
region. Our results are consistent with the Gaussian and bimodal coupling
distributions being in the same universality class.Comment: 11 pages, including 6 postscript figures. Latex with revtex macro
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
Study of Chirality in the Two-Dimensional XY Spin Glass
We study the chirality in the Villain form of the XY spin glass in
two--dimensions by Monte Carlo simulations. We calculate the chiral-glass
correlation length exponent and find that
in reasonable agreement with
earlier studies. This indicates that the chiral and phase variables are
decoupled on long length scales and diverge as with {\em different}
exponents, since the spin-glass correlation length exponent was found, in
earlier studies, to be about 1.0.Comment: 4 pages. Latex file and 4 embedded postscript files are included in a
self-unpacking compressed tar file. A postscript version is available at
ftp://chopin.ucsc.edu/pub/xysg.p
Temperature Chaos in Two-Dimensional Ising Spin Glasses with Binary Couplings: a Further Case for Universality
We study temperature chaos in a two-dimensional Ising spin glass with random
quenched bimodal couplings, by an exact computation of the partition functions
on large systems. We study two temperature correlators from the total free
energy and from the domain wall free energy: in the second case we detect a
chaotic behavior. We determine and discuss the chaos exponent and the fractal
dimension of the domain walls.Comment: 5 pages, 6 postscript figures; added reference
Disorder chaos in spin glasses
We investigate numerically disorder chaos in spin glasses, i.e. the
sensitivity of the ground state to small changes of the random couplings. Our
study focuses on the Edwards-Anderson model in d=1,2,3 and in mean-field. We
find that in all cases, simple scaling laws, involving the size of the system
and the strength of the perturbation, are obeyed. We characterize in detail the
distribution of overlap between ground states and the geometrical properties of
flipped spin clusters in both the weak and strong chaos regime. The possible
relevance of these results to temperature chaos is discussed.Comment: 7 pages, 8 figures, replaced with accepted versio
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
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
A real space renormalization group approach to spin glass dynamics
The slow non-equilibrium dynamics of the Edwards-Anderson spin glass model on
a hierarchical lattice is studied by means of a coarse-grained description
based on renormalization concepts. We evaluate the isothermal aging properties
and show how the occurrence of temperature chaos is connected to a gradual loss
of memory when approaching the overlap length. This leads to rejuvenation
effects in temperature shift protocols and to rejuvenation--memory effects in
temperature cycling procedures with a pattern of behavior parallel to
experimental observations.Comment: 4 pages, 4 figure