Bolthausen: Spin Glasses

 

Lecture: Thursdays 9-11, TU, IRTG lounge MA 748. The last lecture was on 8 July 2010.

 

The program is:

•  1 Preliminary topics
  • 1.1 Properties of Gaussian variables (Concentration, Wick's theorem)
  • 1.2 Classical mean field models
  • 1.3 Point processes
•   2 The Sherrington-Kirkpatrick model: First properties
  • 2.1 Existence of the free energy
  • 2.2 Guerra's replica symmetric bound
  • 2.3 The high temperature ("replica symmetric") solution
  • 2.4 The Thouless-Anderson-Palmer equations
•   3 Ruelle cascades and the BS-coalescent
•   4 The Aizenman-Sims-Starr random overlap structures and Guerra's replica breaking bound
•   5 Ultrametricity
  • 5.1 The Ghirlanda-Guerra identities
  • 5.2 Panchenko's ultrametricity result
  • 5.3 Ultrametricity in the non-hierarchical random energy model

Lecture notes:

• updated manuscript, June 30