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

Abstract : We join with the other contributors to this special issue of JSP to acknowledge the many contributions to Mathematical and Statistical Physics made over the years by Juerg Froehlich, Tom Spencer and Herbert Spohn. May they each live and be well to one hundred twenty. 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 θ ∈ [−π/2, +π/2]; here θ 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 results – in particular, there is at least one pure state for each θ.
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Douglas Abraham, Charles Newman, Senya Shlosman. A continuum of pure states in the Ising model on a halfplane. Journal of Statistical Physics, Springer Verlag, 2018, 172 (2), pp.611-626. ⟨10.1007/s10955-017-1918-4⟩. ⟨hal-01648384⟩

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