Spin-glass theory for pedestrians

Abstract

In these notes the main theoretical concepts and techniques in the field of mean-field spinglasses are reviewed in a compact and pedagogical way, for the benefit of the graduateand undergraduate student. One particular spin-glass model is analysed (thep-spin spherical model) by using three different approaches: thermodynamics, coveringpure states, overlaps, overlap distribution, replica symmetry breaking, and thestatic transition; dynamics, covering the generating functional method, generalizedLangevin equation, equations for the correlation and the response, the modecoupling approximation, and the dynamical transition; and finally complexity,covering the mean-field (Thouless–Anderson–Palmer) free energy, metastable states,entropy crisis, threshold energy, and saddles. Particular attention has been paidto the mutual consistency of the results obtained from the different methods.