The metastate approach to thermodynamic chaos

TL;DR

This paper introduces a metastate-based framework for understanding thermodynamic chaos in disordered systems like spin glasses, addressing limitations of traditional order parameters and unifying concepts such as replica symmetry breaking and chaotic size dependence.

Contribution

It proposes a metastate approach to describe complex thermodynamic structures, replacing the mean-field picture and linking various phenomena in disordered systems.

Findings

Metastate formalism captures thermodynamic complexity in disordered systems.

Unifies concepts like replica symmetry breaking and chaotic size dependence.

Classifies possible metastates for the Edwards-Anderson model.

Abstract

In realistic disordered systems, such as the Edwards-Anderson (EA) spin glass, no order parameter, such as the Parisi overlap distribution, can be both translation-invariant and non-self-averaging. The standard mean-field picture of the EA spin glass phase can therefore not be valid in any dimension and at any temperature. Further analysis shows that, in general, when systems have many competing (pure) thermodynamic states, a single state which is a mixture of many of them (as in the standard mean-field picture) contains insufficient information to reveal the full thermodynamic structure. We propose a different approach, in which an appropriate thermodynamic description of such a system is instead based on a metastate, which is an ensemble of (possibly mixed) thermodynamic states. This approach, modelled on chaotic dynamical systems, is needed when chaotic size dependence (of finite volume correlations) is present. Here replicas arise in a natural way, when a metastate is specified by its (meta)correlations. The metastate approach explains, connects, and unifies such concepts as replica symmetry breaking, chaotic size dependence and replica non-independence. Furthermore, it replaces the older idea of non-self-averaging as dependence on the bulk couplings with the concept of dependence on the state within the metastate at fixed coupling realization. We use these ideas to classify possible metastates for the EA model, and discuss two scenarios introduced by us earlier --- a nonstandard mean-field picture and a picture intermediate between that and the usual scaling/droplet picture.