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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 We consider the Edwards-Anderson Ising spin glass model on the half-plane $${\mathbb{Z} \times \mathbb{Z}^+}$$ 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 $${\mathcal{K}(J,\alpha)}$$ of couplings J and ground state pairs α 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 $${\mathcal{K}(\alpha\,|\,J)}$$ is supported on a single ground state pair. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Communications in Mathematical Physics Springer Journals

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

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References (20)

Publisher
Springer Journals
Copyright
Copyright © 2010 by Springer-Verlag
Subject
Physics; Classical and Quantum Gravitation, Relativity Theory; Statistical Physics, Dynamical Systems and Complexity; Quantum Physics; Theoretical, Mathematical and Computational Physics
ISSN
0010-3616
eISSN
1432-0916
DOI
10.1007/s00220-010-1130-8
Publisher site
See Article on Publisher Site

Abstract

We consider the Edwards-Anderson Ising spin glass model on the half-plane $${\mathbb{Z} \times \mathbb{Z}^+}$$ 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 $${\mathcal{K}(J,\alpha)}$$ of couplings J and ground state pairs α 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 $${\mathcal{K}(\alpha\,|\,J)}$$ is supported on a single ground state pair.

Journal

Communications in Mathematical PhysicsSpringer Journals

Published: Sep 10, 2010

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