Nonrealistic Behavior of Mean Field Spin Glasses

Abstract

We study chaotic size dependence of the low temperature correlations in the SK spin glass. We prove that as temperature scales to zero with volume, for any typical coupling realization, the correlations cycle through every spin configuration in every fixed observation window. This cannot happen in short-ranged models as there it would mean that every spin configuration is an infinite-volume ground state. Its occurrence in the SK model means that the commonly used `modified clustering' notion of states sheds little light on the RSB solution of SK, and conversely, the RSB solution sheds little light on the thermodynamic structure of EA models.