2005/05/02 by Tommaso Castellani, Andrea Cavagna · 1 citation
Physics and Astronomy · #cond-mat.dis-nn #cond-mat.stat-mech
paper · pdf · doi:10.1088/1742-5468/2005/05/p05012
published as J. Stat. Mech. (2005) P05012 · Lecture notes of the school: "Unifying Concepts in Glassy Physics III", Bangalore, June 2004
arxiv created 2005/05/02 · arxiv updated 2009/12/01
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.