Mathematics – Probability

Scientific paper

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2009-11-21

Commun. Math. Phys., Vol. 300 (2010) no. 3, 641-657

Mathematics

Probability

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.

**Arguin Louis-Pierre**

Mathematics – Probability

Scientist

**Damron Michael**

Mathematics – Probability

Scientist

**Newman Charles**

Mathematics – Probability

Scientist

**Stein Daniel**

Mathematics – Probability

Scientist

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