Non-normal asymptotics of the mean-field Heisenberg model

I will discuss spin models of magnets and superconductors, with spins in the 
circle (XY model) and in the sphere (Heisenberg model), that exhibit interesting 
phase transitions. I will discuss work with Elizabeth Meckes on the mean-field 
Heisenberg model and its non-normal behavior at the phase transition. There is 
much that is still mysterious about these models:  
I'll mention work in progress with Tayyab Nawaz and Leslie Ross.