Critical and Disordered Systems at ICTP-SAIFR

Statistical mechanics of disordered systems

Half-course, summer 2026 · Course description

Lecture notes

1. Introduction & motivation
2. Equilibrium statistical mechanics: the Curie–Weiss model
3. The spherical spin glasses – annealed average
4. The replica method and replica symmetry
5. Stability of replica symmetry and replica symmetry breaking
6. Dynamics: the cavity method and equilibrium
7. Dynamics: aging
8. Complexity of metastable states
9. Franz–Parisi potential

Exercises

1. Mathematical prerequisites
2. Equilibrium statistical mechanics
3. Annealed averages & Langevin equations
4. Replica symmetry for Sherrington–Kirkpatrick
5. Replica symmetry breaking for Sherrington–Kirkpatrick
6. The fluctuation-dissipation theorem
7. DMFT by path integration
8. Spin glass theory and beyond