Course: Spin glasses by Francesco Zamponi

Main topics

• Spin glasses: definitions and applications
  • Spin glasses on a generic graph
  • Materials: real spin glasses, propagation of light in disordered cavities
  • Optimization problems and diluted graphs
  • Basic concepts: Disorder, self-averaging, annealed-quenched averages, pure states, overlap, aging
• Mean field theory of spin glasses. The SK model.
  • The fully connected spherical p-spin model: statics and equilibrium dynamics
  • Sketch of the Parisi solution of the SK model
  • Out of equilibrium dynamics and aging
• Spin glasses on diluted graphs and optimization problems; clustering of solutions, freezing of variables, condensation and SAT/UNSAT transition
  • Clustering in the k-XORSAT problem: leaf removal algorithm
  • Phase transitions in k-SAT and k-COL: the cavity method
  • Relation with algorithmic (dynamical) phase transitions
• Finite dimensional spin glasses (sketchy)
  • The EA model and the debate on the nature of the low-temperature phase
  • Structural glasses: Random First Order Theory, Nucleation and Kac models
• Numerical methods

Lecture notes