L. A. Caffarelli, R. de la Llave
Interfaces of ground states in Ising models with periodic coefficients
(285K, pdf)

ABSTRACT.  We study the interfaces of ground states of ferromagnetic Ising models 
with external fields. 
We show that, if the coefficients of the interaction and the magnetic field 
are periodic, the magnetic field has zero flux over a period and is small 
enough, then for every plane, we can find a ground state whose interface 
lies at a bounded distance of the plane. 
This bound on the width of the interface can be chosen independent of the 
plane. 
We also study the average energy of the plane-like 
 interfaces as a function of 
the direction. We show that there is a well defined thermodynamic 
limit and that it enjoys several convexity properties.