Introduction to the SK model
Dmitry Panchenko · Current Developments in Mathematics · 2014
This paper is an overview of recent advances in spin glass models.Main focus is on the Sherrington-Kirkpatrick model and, in particular, on the results that explain the origin of various hypotheses at the centre of the well-established theory of spin glasses in physics, concerning the fine structure of the Gibbs measure.Contents 1.The Sherrington-Kirkpatrick model 2. The Parisi formula 3. Beyond the Sherrington-Kirkpatrick model 4. Before and after the Parisi solution 5. Asymptotic Gibbs distributions 6. Structure of asymptotic Gibbs distributions 7. Overview of results 8. Miscellaneous Gaussian techniques 9.The Ghirlanda-Guerra identities 10.Ultrametricity 11.Reconstructing the limit 12. Sketch of proof of the Parisi formula 13.Phase transition 14.Some open problems References