Thermodynamic Chaos and the Structure of Short-Range Spin Glasses

This paper presents an approach, recently introduced by the authors and based on the notion of “metastates,” to the chaotic size dependence expected in systems with many competing pure states and applies it to the Edwards-Anderson (EA) spin glass model. We begin by reviewing the standard picture of the EA model based on the Sherrington-Kirkpatrick (SK) model and why that standard SK picture is untenable. Then we introduce metastates, which are the analogues of the invariant probability measures describing chaotic dynamical systems and discuss how they should appear in several models simpler than the EA spin glass. Finally, we consider possibilities for the nature of the EA metastate, including one which is a nonstandard SK picture, and speculate on their prospects. An appendix contains proofs used in our construction of metastates and in the earlier construction by Aizenman and Wehr.