%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 }