# Uniqueness of Ground States for Short-Range Spin Glasses in the Half-Plane

Mathematics – Probability

Scientific paper

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## Details Uniqueness of Ground States for Short-Range Spin Glasses in the Half-Plane Uniqueness of Ground States for Short-Range Spin Glasses in the Half-Plane

20 pages, 3 figures

Scientific paper

We consider the Edwards-Anderson Ising spin glass model on the half-plane $Z \times Z^+$ with zero external field and a wide range of choices, including mean zero Gaussian, for the common distribution of the collection J of i.i.d. nearest neighbor couplings. The infinite-volume joint distribution $K(J,\alpha)$ of couplings J and ground state pairs $\alpha$ with periodic (respectively, free) boundary conditions in the horizontal (respectively, vertical) coordinate is shown to exist without need for subsequence limits. Our main result is that for almost every J, the conditional distribution $K(\alpha|J)$ is supported on a single ground state pair.

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