 0088 F. Baffioni, F. Rosati
 SOME EXACT RESULTS ON THE ULTRAMETRIC OVERLAP DISTRIBUTION
IN MEAN FIELD SPIN GLASS MODELS (I)
(60K, latex )
Feb 25, 00

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Abstract. The mean field spin glass model is analyzed by a combination of
mathematically rigororous methods and a powerful {\it Ansatz}.
The method exploited is general, and can be applied to others
disordered mean fiel models such as, {\it e.g.}, neural networks.
It is well known that the probability measure of overlaps among replicas
carries the whole physical content of these models.
A functional order parameter of Parisi type is introduced by
rigorous methods, according to previous works by F.~Guerra.
By the {\it Ansatz} that the functional order parameter is the correct
order parameter of the model, we explicitly find the full overlap
distribution.The physical interpretation of the functional order
parameter is obtained, and ultrametricity of overlaps is derived as
a natural consequence of a branching diffusion process.
It is shown by explicit construction that
ultrametricity of the 3replicas overlap distribution
together with the GhirlandaGuerra relations determines the
distribution of overlaps among $s$ replicas, for any $s$, in terms of
the oneoverlap distribution.
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