Spin-Glass Theory for Pedestrians

Abstract

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.

Lecture notes of the school: "Unifying Concepts in Glassy Physics III", Bangalore, June 2004

References in corpus (21)

• Testing Mode-Coupling Theory for a Supercooled Binary Lennard-Jones Mixture I: The van Hove Correlation Function
• Analytical Solution of the Off-Equilibrium Dynamics of a Long Range Spin-Glass Model
• Scaling behavior in the $\beta$-relaxation regime of a supercooled Lennard-Jones mixture
• Testing Mode-Coupling Theory for a Supercooled Binary Lennard-Jones Mixture II: Intermediate Scattering Function and Dynamic Susceptibility
• Mode-Coupling Theory (MCT) Lecture Notes
• Mode-Coupling Approximations, Glass Theory and Disordered Systems
• Saddles in the energy landscape probed by supercooled liquids
• Saddle Points and Dynamics of Lennard-Jones Clusters, Solids and Supercooled Liquids
• Energy landscape of a Lennard-Jones liquid: Statistics of stationary points
• Phase space geometry and slow dynamics
• On the stationary points of the TAP free energy
• Geometric approach to the dynamic glass transition
• Quasi-equilibrium interpretation of aging dynamics
• Fragile vs strong liquids: a saddles ruled scenario
• On Mean Field Glassy Dynamics out of Equilibrium
• Role of saddles in mean-field dynamics above the glass transition
• Index Distribution of Random Matrices with an Application to Disordered Systems
• Number of solutions of the TAP equations for p--spin interaction spin glasses
• A Crash Course on Aging
• Supersymmetric quenched complexity in the Sherrington-Kirkpatrick model
• A single saddle model for the beta-relaxation in supercooled liquids

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