TY - JOUR

T1 - Uniqueness of Ground States for Short-Range Spin Glasses in the Half-Plane

AU - Arguin, Louis Pierre

AU - Damron, Michael

AU - Newman, C. M.

AU - Stein, D. L.

PY - 2010/12

Y1 - 2010/12

N2 - We consider the Edwards-Anderson Ising spin glass model on the half-plane ℤ × 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,α) 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 K(α{pipe} J) is supported on a single ground state pair.

AB - We consider the Edwards-Anderson Ising spin glass model on the half-plane ℤ × 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,α) 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 K(α{pipe} J) is supported on a single ground state pair.

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U2 - 10.1007/s00220-010-1130-8

DO - 10.1007/s00220-010-1130-8

M3 - Article

AN - SCOPUS:78149500710

SN - 0010-3616

VL - 300

SP - 641

EP - 657

JO - Communications In Mathematical Physics

JF - Communications In Mathematical Physics

IS - 3

ER -