- 04-112 L. A. Caffarelli, R. de la Llave
- Interfaces of ground states in Ising models with periodic coefficients
Apr 15, 04
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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
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.