9,502 research outputs found
Reply to "Comment on Evidence for the droplet picture of spin glasses"
Using Monte Carlo simulations (MCS) and the Migdal-Kadanoff approximation
(MKA), Marinari et al. study in their comment on our paper the link overlap
between two replicas of a three-dimensional Ising spin glass in the presence of
a coupling between the replicas. They claim that the results of the MCS
indicate replica symmetry breaking (RSB), while those of the MKA are trivial,
and that moderate size lattices display the true low temperature behavior. Here
we show that these claims are incorrect, and that the results of MCS and MKA
both can be explained within the droplet picture.Comment: 1 page, 1 figur
Velocity Distribution of Topological Defects in Phase-Ordering Systems
The distribution of interface (domain-wall) velocities in a
phase-ordering system is considered. Heuristic scaling arguments based on the
disappearance of small domains lead to a power-law tail,
for large v, in the distribution of . The exponent p is
given by , where d is the space dimension and 1/z is the growth
exponent, i.e. z=2 for nonconserved (model A) dynamics and z=3 for the
conserved case (model B). The nonconserved result is exemplified by an
approximate calculation of the full distribution using a gaussian closure
scheme. The heuristic arguments are readily generalized to conserved case
(model B). The nonconserved result is exemplified by an approximate calculation
of the full distribution using a gaussian closure scheme. The heuristic
arguments are readily generalized to systems described by a vector order
parameter.Comment: 5 pages, Revtex, no figures, minor revisions and updates, to appear
in Physical Review E (May 1, 1997
Non-equilibrium Phase-Ordering with a Global Conservation Law
In all dimensions, infinite-range Kawasaki spin exchange in a quenched Ising
model leads to an asymptotic length-scale
at because the kinetic coefficient is renormalized by the broken-bond
density, . For , activated kinetics recovers the
standard asymptotic growth-law, . However, at all temperatures,
infinite-range energy-transport is allowed by the spin-exchange dynamics. A
better implementation of global conservation, the microcanonical Creutz
algorithm, is well behaved and exhibits the standard non-conserved growth law,
, at all temperatures.Comment: 2 pages and 2 figures, uses epsf.st
Evidence of non-mean-field-like low-temperature behavior in the Edwards-Anderson spin-glass model
The three-dimensional Edwards-Anderson and mean-field Sherrington-Kirkpatrick
Ising spin glasses are studied via large-scale Monte Carlo simulations at low
temperatures, deep within the spin-glass phase. Performing a careful
statistical analysis of several thousand independent disorder realizations and
using an observable that detects peaks in the overlap distribution, we show
that the Sherrington-Kirkpatrick and Edwards-Anderson models have a distinctly
different low-temperature behavior. The structure of the spin-glass overlap
distribution for the Edwards-Anderson model suggests that its low-temperature
phase has only a single pair of pure states.Comment: 4 pages, 6 figures, 2 table
Persistence in systems with algebraic interaction
Persistence in coarsening 1D spin systems with a power law interaction
is considered. Numerical studies indicate that for sufficiently
large values of the interaction exponent ( in our
simulations), persistence decays as an algebraic function of the length scale
, . The Persistence exponent is found to be
independent on the force exponent and close to its value for the
extremal () model, . For smaller
values of the force exponent (), finite size effects prevent the
system from reaching the asymptotic regime. Scaling arguments suggest that in
order to avoid significant boundary effects for small , the system size
should grow as .Comment: 4 pages 4 figure
Zero Temperature Dynamics of the Weakly Disordered Ising Model
The Glauber dynamics of the pure and weakly disordered random-bond 2d Ising
model is studied at zero-temperature. A single characteristic length scale,
, is extracted from the equal time correlation function. In the pure
case, the persistence probability decreases algebraically with the coarsening
length scale. In the disordered case, three distinct regimes are identified: a
short time regime where the behaviour is pure-like; an intermediate regime
where the persistence probability decays non-algebraically with time; and a
long time regime where the domains freeze and there is a cessation of growth.
In the intermediate regime, we find that , where
. The value of is consistent with that
found for the pure 2d Ising model at zero-temperature. Our results in the
intermediate regime are consistent with a logarithmic decay of the persistence
probability with time, , where .Comment: references updated, very minor amendment to abstract and the
labelling of figures. To be published in Phys Rev E (Rapid Communications), 1
March 199
Real space analysis of inherent structures
We study a generalization of the one-dimensional disordered Potts model,
which exhibits glassy properties at low temperature. The real space properties
of inherent structures visited dynamically are analyzed through a decomposition
into domains over which the energy is minimized. The size of these domains is
distributed exponentially, defining a characteristic length scale which grows
in equilibrium when lowering temperature, as well as in the aging regime at a
given temperature. In the low temperature limit, this length can be interpreted
as the distance between `excited' domains within the inherent structures.Comment: 7 pages, 8 figures, final versio
Evidence for the droplet/scaling picture of spin glasses
We have studied the Parisi overlap distribution for the three dimensional
Ising spin glass in the Migdal-Kadanoff approximation. For temperatures T
around 0.7Tc and system sizes upto L=32, we found a P(q) as expected for the
full Parisi replica symmetry breaking, just as was also observed in recent
Monte Carlo simulations on a cubic lattice. However, for lower temperatures our
data agree with predictions from the droplet or scaling picture. The failure to
see droplet model behaviour in Monte Carlo simulations is due to the fact that
all existing simulations have been done at temperatures too close to the
transition temperature so that sytem sizes larger than the correlation length
have not been achieved.Comment: 4 pages, 6 figure
Phase Ordering Kinetics with External Fields and Biased Initial Conditions
The late-time phase-ordering kinetics of the O(n) model for a non-conserved
order parameter are considered for the case where the O(n) symmetry is broken
by the initial conditions or by an external field. An approximate theoretical
approach, based on a `gaussian closure' scheme, is developed, and results are
obtained for the time-dependence of the mean order parameter, the pair
correlation function, the autocorrelation function, and the density of
topological defects [e.g. domain walls (), or vortices ()]. The
results are in qualitative agreement with experiments on nematic films and
related numerical simulations on the two-dimensional XY model with biased
initial conditions.Comment: 35 pages, latex, no figure
Growth Laws for Phase Ordering
We determine the characteristic length scale, , in phase ordering
kinetics for both scalar and vector fields, with either short- or long-range
interactions, and with or without conservation laws. We obtain
consistently by comparing the global rate of energy change to the energy
dissipation from the local evolution of the order parameter. We derive growth
laws for O(n) models, and our results can be applied to other systems with
similar defect structures.Comment: 12 pages, LaTeX, second tr
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