430 research outputs found
Stochastic Stability: a Review and Some Perspectives
A review of the stochastic stability property for the Gaussian spin glass
models is presented and some perspectives discussed.Comment: 12 pages, typos corrected, references added. To appear in Journal of
Statistical Physics, Special Issue for the 100th Statistical Mechanics
Meetin
Stochastic Stability and the Spin Glass Phase. The State of the Art for Mean Field and Finite Dimensional Models
Some invariances under perturbations of the spin glass phase are introduced,
their proofs outlined and their consequences illustrated as factorisation rules
for the overlap distribution. A comparison between the state of the art for
mean field and finite dimensional models is shortly discussed.Comment: Invited address at the International Congress on Mathematical
Physics, Aalborg 2012, Denmar
Inequalities for the Local Energy of Random Ising Models
We derive a rigorous lower bound on the average local energy for the Ising
model with quenched randomness. The result is that the lower bound is given by
the average local energy calculated in the absence of all interactions other
than the one under consideration. The only condition for this statement to hold
is that the distribution function of the random interaction under consideration
is symmetric. All other interactions can be arbitrarily distributed including
non-random cases. A non-trivial fact is that any introduction of other
interactions to the isolated case always leads to an increase of the average
local energy, which is opposite to ferromagnetic systems where the Griffiths
inequality holds. Another inequality is proved for asymmetrically distributed
interactions. The probability for the thermal average of the local energy to be
lower than that for the isolated case takes a maximum value on the Nishimori
line as a function of the temperature. In this sense the system is most stable
on the Nishimori line.Comment: 10 pages. Submitted to J. Phys. Soc. Jp
Interaction Flip Identities for non Centered Spin Glasses
We consider spin glass models with non-centered interactions and investigate
the effect, on the random free energies, of flipping the interaction in a
subregion of the entire volume. A fluctuation bound obtained by martingale
methods produces, with the help of integration by parts technique, a family of
polynomial identities involving overlaps and magnetizations
Modeling Society with Statistical Mechanics: an Application to Cultural Contact and Immigration
We introduce a general modeling framework to predict the outcomes, at the
population level, of individual psychology and behavior. The framework
prescribes that researchers build a cost function that embodies knowledge of
what trait values (opinions, behaviors, etc.) are favored by individual
interactions under given social conditions. Predictions at the population level
are then drawn using methods from statistical mechanics, a branch of
theoretical physics born to link the microscopic and macroscopic behavior of
physical systems. We demonstrate our approach building a model of cultural
contact between two cultures (e.g., immigration), showing that it is possible
to make predictions about how contact changes the two cultures
Local Order at Arbitrary Distances in Finite-Dimensional Spin-Glass Models
For a finite dimensional spin-glass model we prove local order at low
temperatures for both local observables and for products of observables at
arbitrary mutual distance. When the Hamiltonian includes the Edwards-Anderson
interaction we prove "bond" local order, when it includes the random-field
interaction we prove "site" local order
On the Stability of the Quenched State in Mean Field Spin Glass Models
While the Gibbs states of spin glass models have been noted to have an
erratic dependence on temperature, one may expect the mean over the disorder to
produce a continuously varying ``quenched state''. The assumption of such
continuity in temperature implies that in the infinite volume limit the state
is stable under a class of deformations of the Gibbs measure. The condition is
satisfied by the Parisi Ansatz, along with an even broader stationarity
property. The stability conditions have equivalent expressions as marginal
additivity of the quenched free energy. Implications of the continuity
assumption include constraints on the overlap distribution, which are expressed
as the vanishing of the expectation value for an infinite collection of
multi-overlap polynomials. The polynomials can be computed with the aid of a
"real"-replica calculation in which the number of replicas is taken to zero.Comment: 17 pages, LaTex, Revised June 5, 199
Thermodynamic Limit for Spin Glasses. Beyond the Annealed Bound
Using a correlation inequality of Contucci and Lebowitz for spin glasses, we
demonstrate existence of the thermodynamic limit for short-ranged spin glasses,
under weaker hypotheses than previously available, namely without the
assumption of the annealed bound.Comment: 8 page
The Ghirlanda-Guerra Identities
If the variance of a Gaussian spin-glass Hamiltonian grows like the volume
the model fulfills the Ghirlanda-Guerra identities in terms of the normalized
Hamiltonian covariance.Comment: 18 page
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