Mathematical aspects of mean field spin glass theory
| dc.creator | Guerra, F. | |
| dc.date | 2004-10-18 | |
| dc.date.accessioned | 2026-07-07T06:21:19Z | |
| dc.date.available | 2026-07-07T06:21:19Z | |
| dc.description | A comprehensive review will be given about the rich mathematical structure of mean field spin glass theory, mostly developed, until now, in the frame of the methods of theoretical physics, based on deep physical intuition and hints coming from numerical simulation. Central to our treatment is a very simple and yet powerful interpolation method, allowing to compare different probabilistic schemes, by using convexity and positivity arguments. In this way we can prove the existence of the thermodynamic limit for the free energy density of the system, a long standing open problem. Moreover, in the frame of a generalized variational principle, we can show the emergency of the Derrida-Ruelle random probability cascades, leading to the form of free energy given by the celebrated Parisi \textit {Ansatz}. All these results seem to be in full agreement with the mechanism of spontaneous replica symmetry breaking as developed by Giorgio Parisi. | |
| dc.description | proceedings of the "4th European Congress of Mathematics", Stockholm, 2004. 17 pages | |
| dc.identifier | https://arxiv.org/abs/cond-mat/0410435 | |
| dc.identifier | http://arxiv.org/abs/cond-mat/0410435 | |
| dc.identifier | European Congress of Mathematics, Stockolm, June 27-July 2, 2004, Ari Laptev, Editor, European Mathematical Society, Zurich, 2005. | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/95560 | |
| dc.subject | Disordered Systems and Neural Networks | |
| dc.subject | Mathematical Physics | |
| dc.title | Mathematical aspects of mean field spin glass theory | |
| dc.type | text |