Current Developments in Mathematics
Introduction to the SK model
Pages: 231 – 291
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.
spin glasses, free energy, Parisi formula, ultrametricity
2010 Mathematics Subject Classification
60F10, 60G09, 60G15, 60K35, 82B44