Speaker : Christof Külske

Title: On localized and delocalized infinite-volume states for gradient models on 
trees 

Abstract:  We consider spin systems with gradient interactions on infinite regular 
trees. 
These are integer-valued spin-models, where the spins (also called height variables) 
interact via a height-shift invariant interaction, between nearest neighbors on the 
tree. 
We construct different types of infinite-volume states: 
States which localize at given finite heights, and more generally 
states which localize on finite subsets A of the local state space.  
We also discuss related existence results for delocalized states, 
and show that they may coexist with the localized ones at the same parameter 
values of the model, in regimes of low enough temperature. 

Joint works 
with Florian Henning, Alberto Abbondandolo, Pietro Majer, Arnaud Le Ny, Loren 
Coquille, Utkir Rozikov.