Abstract
We study the Ising andN-vector spin glasses with exchange couplings J=(J ij ;i, jεZ d), which are independent random variables with EJij=0 andEJ n ij ⩽γ n n!¦i−j¦ −nαd, fornεℕ, some finite constant γ>0, and α>1/2. For sufficiently smallβ, we show that forE-a.a.J there is a weakly unique, extremal, infinite-volume Gibbs measure μβJ for which the expectation of a single (component of) spin vanishes and which has the cluster property inL 2(E) with the same decay as interaction. This work is based on results and methods of Fröhlich and Zegarlinski.
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Zegarlinski, B. Spin glasses with long-range interaction at high temperatures. J Stat Phys 47, 911–930 (1987). https://doi.org/10.1007/BF01206165
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DOI: https://doi.org/10.1007/BF01206165