Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
2005-05-02
J. Stat. Mech. (2005) P05012
Physics
Condensed Matter
Disordered Systems and Neural Networks
Lecture notes of the school: "Unifying Concepts in Glassy Physics III", Bangalore, June 2004
Scientific paper
10.1088/1742-5468/2005/05/P05012
In these notes the main theoretical concepts and techniques in the field of mean-field spin-glasses are reviewed in a compact and pedagogical way, for the benefit of the graduate and undergraduate student. One particular spin-glass model is analyzed (the p-spin spherical model) by using three different approaches. Thermodynamics, covering pure states, overlaps, overlap distribution, replica symmetry breaking, and the static transition. Dynamics, covering the generating functional method, generalized Langevin equation, equations for the correlation and the response, the Mode Coupling approximation, and the dynamical transition. And finally complexity, covering the mean-field (TAP) free energy, metastable states, entropy crisis, threshold energy, and saddles. Particular attention has been paid on the mutual consistency of the results obtained from the different methods.
Castellani Tommaso
Cavagna Andrea
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