Short-Range Spin Glasses: The Metastate Approach

The nature of the low-temperature spin glass phase in short-range models remains one of the central problems in the statistical mechanics of disordered systems (Binder and Young 1986, Chowdhury 1986, Mézard et al. 1987, Stein 1989, Fischer and Hertz 1991, Dotsenko 2001, Newman and Stein 2003). While many of the basic questions remain unanswered, analytical and rigorous work over the past decade have greatly streamlined the number of possible scenarios for pure state structure and organization at low temperatures, and have clarified the thermodynamic behavior of these systems.