METASTATE APPROACH TO THERMODYNAMIC CHAOS

In realistic disordered systems, such as the Edwards-Anderson (EA) spi n 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 va lid in any dimension and at any temperature. Further analysis shows th at, in general, when systems have many competing (pure) thermodynamic states, a single state which is a mixture of many of them (as in the s tandard mean-field picture) contains insufficient information to revea l the full thermodynamic structure. We propose a different approach, i n which an appropriate thermodynamic description of such a system is i nstead based on a metastate, which is an ensemble of (possibly mixed) thermodynamic states. This approach, modeled on chaotic dynamical syst ems, is needed when chaotic size dependence (of finite volume correlat ions) is present. Here replicas arise in a natural way, when a metasta te is specified by its (meta)correlations. The metastate approach expl ains, connects, and unifies such concepts as replica symmetry breaking , chaotic size dependence and replica nonindependence. Furthermore, it replaces the older idea of non-self-averaging as dependence on the bu lk couplings with the concept of dependence on the state within the me tastate at fixed coupling realization. We use these ideas to classify possible metastates for the EA model, and discuss two scenarios introd uced by us earlier-a nonstandard mean-field picture and a picture inte rmediate between that and the usual scaling-droplet picture.