Silvio Franz, Francesca Tria — A Note on the Guerra and Talagrand Theorems for Mean Field Spin Glasses: The Simple Case of Spherical Models
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Название: A Note on the Guerra and Talagrand Theorems for Mean Field Spin Glasses: The Simple Case of Spherical Models
Авторы: Silvio Franz, Francesca Tria
Аннотация:
The aim of this paper is to discuss the main ideas of the Talagrand proof of the Parisi
Ansatz for the free-energy of Mean Field Spin Glasses with a physicist’s approach. We
consider the case of the spherical p-spin model, which has the following advantages:
(1) the Parisi Ansatz takes the simple “one step replica symmetry breaking form,” (2)
the replica free-energy as a function of the order parameters is simple enough to allow
for numerical maximization with arbitrary precision. We present the essential ideas of
the proof, we stress its connections with the theory of effective potentials for glassy
systems, and we reduce the technically more difficult part of the Talagrand’s analysis to
an explicit evaluation of the solution of a variational problem
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