Exact results on mean field spin glass models.
Francesco Rosati
Abstract
The mean field spin glass model is analyzed by a combination of
exact methods and a powerful {it Ansatz}.
The method exploited is general, and can be applied to others
disordered mean field 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 3-replicas overlap distribution
together with the Ghirlanda--Guerra relations determines the distribution
of overlaps among $s$ replicas, for any $s$, in terms of
the one-overlap distribution.
Elenco dei partecipanti al convegno di Bari.