caa a22 4500 467892830 CHVBK 20180406152754.0 cr unu---uuuuu 170328e20060101xx s 000 0 eng 10.1007/s10955-005-8007-9 doi (NATIONALLICENCE)springer-10.1007/s10955-005-8007-9 A Note on the Guerra and Talagrand Theorems for Mean Field Spin Glasses: The Simple Case of Spherical Models [Elektronische Daten] [Silvio Franz, Francesca Tria] 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. Springer Science + Business Media, Inc., 2006 Spin glasses nationallicence Mean field theory nationallicence Replica method nationallicence Interpolation method nationallicence Franz Silvio The Abdus Salam International Center for Theoretical Physics, Strada Costiera 11, P.O. Box 563, I-34100, Italy, Trieste aut Tria Francesca The Abdus Salam International Center for Theoretical Physics, Strada Costiera 11, P.O. Box 563, I-34100, Italy, Trieste aut Journal of Statistical Physics Kluwer Academic Publishers-Plenum Publishers 122/2(2006-01-01), 313-332 0022-4715 122:2<313 2006 122 10955 https://doi.org/10.1007/s10955-005-8007-9 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10955-005-8007-9 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Franz Silvio The Abdus Salam International Center for Theoretical Physics, Strada Costiera 11, P.O. Box 563, I-34100, Italy, Trieste aut NATIONALLICENCE 700 1- Tria Francesca The Abdus Salam International Center for Theoretical Physics, Strada Costiera 11, P.O. Box 563, I-34100, Italy, Trieste aut NATIONALLICENCE 773 0- Journal of Statistical Physics Kluwer Academic Publishers-Plenum Publishers 122/2(2006-01-01), 313-332 0022-4715 122:2<313 2006 122 10955 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer