45 research outputs found
Numerical study of the dynamics of some long range spin glass models
We present results of a Monte Carlo study of the equilibrium dynamics of the
one dimensional long-range Ising spin glass model. By tuning a parameter
, this model interpolates between the mean field
Sherrington-Kirkpatrick model and a proxy of the finite dimensional
Edward-Anderson model. Activated scaling fits for the behavior of the
relaxation time as a function of the number of spins (Namely
) give values of that are not stable against
inclusion of subleading corrections. Critical scaling ()
gives more stable fits, at least in the non mean field region. We also present
results on the scaling of the time decay of the critical remanent magnetization
of the Sherrington-Kirkpatrick model, a case where the simulation can be done
with quite large systems and that shows the difficulties in obtaining precise
values for dynamical exponents in spin glass models
Rare events analysis of temperature chaos in the Sherrington-Kirkpatrick model
We investigate the question of temperature chaos in the
Sherrington-Kirkpatrick spin glass model, applying to existing Monte Carlo data
a recently proposed rare events based data analysis method. Thanks to this new
method, temperature chaos is now observable for this model, even with the
limited size systems that can be currently simulated
Numerical estimate of finite size corrections to the free energy of the SK model using Guerra--Toninelli interpolation
I use an interpolating formula introduced by Guerra and Toninelli to
investigate numerically the finite size corrections to the free energy of the
Sherrington--Kirkpatrick model. The results are compatible with a behavior at , as predicted by Parisi, Ritort and Slanina, and
a behavior below
Dynamics in the Sherrington-Kirkpatrick Ising spin glass at and above Tg
A detailed numerical study is made of relaxation at equilibrium in the
Sherrington-Kirkpatrick Ising spin glass model, at and above the critical
temperature Tg. The data show a long time stretched exponential relaxation q(t)
~ exp[-(t/tau(T))^beta(T)] with an exponent beta(T) tending to ~ 1/3 at Tg. The
results are compared to those which were observed by Ogielski in the 3d ISG
model, and are discussed in terms of a phase space percolation transition
scenario.Comment: 6 pages, 7 figure
What makes slow samples slow in the Sherrington-Kirkpatrick model
Using results of a Monte Carlo simulation of the Sherrington-Kirkpatrick
model, we try to characterize the slow disorder samples, namely we analyze
visually the correlation between the relaxation time for a given disorder
sample with several observables of the system for the same disorder sample.
For temperatures below but not too low, fast samples (small relaxation
times) are clearly correlated with a small value of the largest eigenvalue of
the coupling matrix, a large value of the site averaged local field probability
distribution at the origin, or a small value of the squared overlap is more robust) . There is a strong correlation between the values of
the relaxation time for two distinct values of the temperature, but this
correlation decreases as the system size is increased. This may indicate the
onset of temperature chaos
Multi-overlap simulations of spin glasses
We present results of recent high-statistics Monte Carlo simulations of the
Edwards-Anderson Ising spin-glass model in three and four dimensions. The study
is based on a non-Boltzmann sampling technique, the multi-overlap algorithm
which is specifically tailored for sampling rare-event states. We thus
concentrate on those properties which are difficult to obtain with standard
canonical Boltzmann sampling such as the free-energy barriers F^q_B in the
probability density P_J(q) of the Parisi overlap parameter q and the behaviour
of the tails of the disorder averaged density P(q) = [P_J(q)]_av.Comment: 14 pages, Latex, 18 Postscript figures, to be published in NIC Series
- Publication Series of the John von Neumann Institute for Computing (NIC
On the Tail of the Overlap Probability Distribution in the Sherrington--Kirkpatrick Model
We investigate the large deviation behavior of the overlap probability
density in the Sherrington--Kirkpatrick model from several analytical
perspectives. First we analyze the spin glass phase using the coupled replica
scheme. Here generically
, and we compute the first correction to the expansion of \A
in powers of . We study also the case, where is know
exactly. Finally we study the paramagnetic phase, where exact results valid for
all 's are obtained. The overall agreement between the various points of
view is very satisfactory. Data from large scale numerical simulations show
that the predicted behavior can be detected already on moderate lattice sizes.Comment: 18 pages including ps figure