Nonrealistic Behavior of Mean Field Spin Glasses

TL;DR

This paper demonstrates that in the SK spin glass model at low temperatures, correlations exhibit chaotic size dependence, cycling through all configurations, which challenges the applicability of traditional state notions and the RSB solution's relevance to short-range models.

Contribution

It proves that the low-temperature correlations in the SK model display chaotic size dependence, contrasting with short-range models and questioning the interpretative power of the RSB solution.

Findings

Correlations cycle through all configurations as temperature approaches zero.

Chaotic size dependence is observed in the SK model.

Traditional notions of states are insufficient to describe the SK model's thermodynamics.

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.