Аннотация
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.
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