Spin-glass theory for pedestrians

Abstract

In these notes the main theoretical concepts and techniques in the field of\nmean-field spin-glasses are reviewed in a compact and pedagogical way, for the\nbenefit of the graduate and undergraduate student. One particular spin-glass\nmodel is analyzed (the p-spin spherical model) by using three different\napproaches. Thermodynamics, covering pure states, overlaps, overlap\ndistribution, replica symmetry breaking, and the static transition. Dynamics,\ncovering the generating functional method, generalized Langevin equation,\nequations for the correlation and the response, the Mode Coupling\napproximation, and the dynamical transition. And finally complexity, covering\nthe mean-field (TAP) free energy, metastable states, entropy crisis, threshold\nenergy, and saddles. Particular attention has been paid on the mutual\nconsistency of the results obtained from the different methods.\n