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 -