A Note on the Guerra and Talagrand Theorems for Mean Field Spin Glasses: The Simple Case of Spherical Models |
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Authors: | Silvio Franz Francesca Tria |
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Institution: | (1) The Abdus Salam International Center for Theoretical Physics, Strada Costiera 11, P.O. Box 563, I-34100, Trieste, Italy |
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Abstract: | 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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Keywords: | Spin glasses Mean field theory Replica method Interpolation method |
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