A continuum of pure states in the Ising model on a halfplane

Abstract

We study the homogeneous nearest-neighbor Ising ferromagnet on the right half plane with a Dobrushin type boundary condition --- say plus on the top part of the boundary and minus on the bottom. For sufficiently low temperature $T$, we completely characterize the pure (i.e., extremal) Gibbs states, as follows. There is exactly one for each angle $\theta \in [-\pi /2,+\pi /2]$; here $\theta$ specifies the asymptotic angle of the interface separating regions where the spin configuration looks like that of the plus (respectively, minus) full-plane state. Some of these conclusions are extended all the way to $T=T_c$ by developing new Ising exact solution result -- in particular, there is at least one pure state for each $\theta$.

In this version, a discussion of the 3D case is included

References in corpus (1)

• Interaction versus entropic repulsion for low temperature Ising polymers