In many spin glass models, due to the symmetry between sites, any limiting
joint distribution of spins under the annealed Gibbs measure admits the
Aldous-Hoover representation encoded by a function $\sigma:
0,1^4\to\-1,+1\$ and one can think of this function as a generic functional
order parameter of the model. In a class of diluted models and in the
Sherrington-Kirkpatrick model, we introduce novel perturbations of the
Hamiltonians that yield certain invariance and self-consistency equations for
this generic functional order parameter and we use these invariance properties
to obtain representations for the free energy in terms of $\sigma$. In the
setting of the Sherrington-Kirkpatrick model the self-consistency equations
imply that the joint distribution of spins is determined by the joint
distributions of the overlaps and we give an explicit formula for $\sigma$
under the Parisi ultrametricity hypothesis. In addition, we discuss some
connections with the Ghirlanda-Guerra identities and stochastic stability.
Beschreibung
Spin glass models from the point of view of spin distributions
%0 Journal Article
%1 Panchenko2010
%A Panchenko, Dmitry
%D 2010
%K glass mathematics physics spin
%T Spin glass models from the point of view of spin distributions
%U http://arxiv.org/abs/1005.2720
%X In many spin glass models, due to the symmetry between sites, any limiting
joint distribution of spins under the annealed Gibbs measure admits the
Aldous-Hoover representation encoded by a function $\sigma:
0,1^4\to\-1,+1\$ and one can think of this function as a generic functional
order parameter of the model. In a class of diluted models and in the
Sherrington-Kirkpatrick model, we introduce novel perturbations of the
Hamiltonians that yield certain invariance and self-consistency equations for
this generic functional order parameter and we use these invariance properties
to obtain representations for the free energy in terms of $\sigma$. In the
setting of the Sherrington-Kirkpatrick model the self-consistency equations
imply that the joint distribution of spins is determined by the joint
distributions of the overlaps and we give an explicit formula for $\sigma$
under the Parisi ultrametricity hypothesis. In addition, we discuss some
connections with the Ghirlanda-Guerra identities and stochastic stability.
@article{Panchenko2010,
abstract = { In many spin glass models, due to the symmetry between sites, any limiting
joint distribution of spins under the annealed Gibbs measure admits the
Aldous-Hoover representation encoded by a function $\sigma:
[0,1]^4\to\{-1,+1\}$ and one can think of this function as a generic functional
order parameter of the model. In a class of diluted models and in the
Sherrington-Kirkpatrick model, we introduce novel perturbations of the
Hamiltonians that yield certain invariance and self-consistency equations for
this generic functional order parameter and we use these invariance properties
to obtain representations for the free energy in terms of $\sigma$. In the
setting of the Sherrington-Kirkpatrick model the self-consistency equations
imply that the joint distribution of spins is determined by the joint
distributions of the overlaps and we give an explicit formula for $\sigma$
under the Parisi ultrametricity hypothesis. In addition, we discuss some
connections with the Ghirlanda-Guerra identities and stochastic stability.
},
added-at = {2010-05-26T00:30:29.000+0200},
author = {Panchenko, Dmitry},
biburl = {https://www.bibsonomy.org/bibtex/23466c1b1715e86fec5460f3cabdd146a/andreab},
description = {Spin glass models from the point of view of spin distributions},
interhash = {bbf5a2f6482f73afed2f6b9741bfe866},
intrahash = {3466c1b1715e86fec5460f3cabdd146a},
keywords = {glass mathematics physics spin},
note = {cite arxiv:1005.2720
},
timestamp = {2010-05-26T00:30:29.000+0200},
title = {Spin glass models from the point of view of spin distributions},
url = {http://arxiv.org/abs/1005.2720},
year = 2010
}