Kuelske, C.
Metastates in disordered mean field models II:
The Superstates
(201K, PS)

ABSTRACT.  We continue to investigate the size dependence of disordered mean 
field models with finite local spin space in more detail, illustrating 
the concept of `superstates', as recently proposed by Bovier and 
Gayrard. We discuss various notions of convergence for the behavior 
of the paths $\left(t\rightarrow \mu_{[t N]}(\eta)\right)_{t\in (0,1]}$ 
in the thermodynamic limit $N\uparrow\infty$. Here $\mu_n(\eta)$ is 
the Gibbs measure in the finite volume $\{1,\dots,n\}$ and $\eta$ 
is the disorder variable. In particular we prove refined convergence 
statements in our concrete examples, the Hopfield model with finitely 
many patterns (having continuous paths) and the Curie Weiss Random 
Field Ising model (having singular paths).