Short-Range Spin Glasses: The Metastate Approach

TL;DR

This paper explores the metastate concept in short-range spin glasses, providing insights into their low-temperature structures and highlighting key open questions in their statistical mechanics.

Contribution

It introduces the metastate approach as a tool to analyze the complex low-temperature behavior of short-range spin glasses, addressing longstanding theoretical challenges.

Findings

Metastate effectively characterizes thermodynamic states in disordered systems.

Identifies fundamental open questions in the structure of spin glasses.

Provides a framework for future research in spin glass theory.

Abstract

We discuss the metastate, a probability measure on thermodynamic states, and its usefulness in addressing difficult questions pertaining to the statistical mechanics of systems with quenched disorder, in particular short-range spin glasses. The possible low-temperature structures of realistic (i.e., short-range) spin glass models are described, and a number of fundamental open questions are presented.