248 research outputs found

### 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 $(1/12 N)
\ln(N/N_0)$ behavior at $T_c$, as predicted by Parisi, Ritort and Slanina, and
a $1/N^{2/3}$ behavior below $T_c$

### 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 $J$ with several observables of the system for the same disorder sample.
For temperatures below $T_c$ 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 $.
Within our limited data, the correlation remains as the system size increases
but becomes less clear as the temperature is decreased (the correlation with$ 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

### 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 $\frac1N \log P_N(q)$ $\approx$ $- {\cal A}$
$((|q|-q_{EA})^3$, and we compute the first correction to the expansion of \A
in powers of $T_c-T$. We study also the $q=1$ case, where $P(q)$ is know
exactly. Finally we study the paramagnetic phase, where exact results valid for
all $q$'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

### 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

### A Determination of Interface Free Energies

We determine the interface free energy $F_{o.d.}$ between disordered and
ordered phases in the q=10 and q=20 2-d Potts models using the results of
multicanonical Monte Carlo simulations on $L^2$ lattices, and suitable finite
volume estimators. Our results, when extrapolated to the infinite volume limit,
agree to high precision with recent analytical calculations. At the transition
point $\beta_t$ the probability distribution function of the energy exhibits
two maxima. Their locations have $1/L^2$ corrections, in contradiction with
claims of $1/L$ behavior made in the literature. Our data show a flat region
inbetween the two maxima which characterizes two domain configurations.Comment: Submited to Nuclear Physics B (FS) Latex file, 24 pages, 11
PostScript figures. Saclay preprint SPhT-93/6

### 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

### Critical Behavior of the Antiferromagnetic Heisenberg Model on a Stacked Triangular Lattice

We estimate, using a large-scale Monte Carlo simulation, the critical
exponents of the antiferromagnetic Heisenberg model on a stacked triangular
lattice. We obtain the following estimates: $\gamma/\nu= 2.011 \pm .014$,
$\nu= .585 \pm .009$. These results contradict a perturbative $2+\epsilon$
Renormalization Group calculation that points to Wilson-Fisher O(4) behaviour.
While these results may be coherent with $4-\epsilon$ results from
Landau-Ginzburg analysis, they show the existence of an unexpectedly rich
structure of the Renormalization Group flow as a function of the dimensionality
and the number of components of the order parameter.Comment: Latex file, 10 pages, 1 PostScript figure. Was posted with a wrong
Title !

### The mean field infinite range p=3 spin glass: equilibrium landscape and correlation time scales

We investigate numerically the dynamical behavior of the mean field 3-spin
spin glass model: we study equilibrium dynamics, and compute equilibrium time
scales as a function of the system size V. We find that for increasing volumes
the time scales $\tau$ increase like $\ln \tau \propto V$. We also present an
accurate study of the equilibrium static properties of the system.Comment: 6 pages, 9 figure

### Large random correlations in individual mean field spin glass samples

We argue that complex systems must possess long range correlations and
illustrate this idea on the example of the mean field spin glass model. Defined
on the complete graph, this model has no genuine concept of distance, but the
long range character of correlations is translated into a broad distribution of
the spin-spin correlation coefficients for almost all realizations of the
random couplings. When we sample the whole phase space we find that this
distribution is so broad indeed that at low temperatures it essentially becomes
uniform, with all possible correlation values appearing with the same
probability. The distribution of correlations inside a single phase space
valley is also studied and found to be much narrower.Comment: Added a few references and a comment phras

### Why temperature chaos in spin glasses is hard to observe

The overlap length of a three-dimensional Ising spin glass on a cubic lattice
with Gaussian interactions has been estimated numerically by transfer matrix
methods and within a Migdal-Kadanoff renormalization group scheme. We find that
the overlap length is large, explaining why it has been difficult to observe
spin glass chaos in numerical simulations and experiment.Comment: 4 pages, 6 figure

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