Abstract
We find the asymptotic decrease of correlations <σ A +y ,σ B >,y∈Z v+1, |y|→∞, in the Ising model at high temperatures. For the case when monomialsσ A andσ B both are odd, using the saddle-point method, we find the asymptotics of the correlations for any dimension ν. For even monomialsσ A ,σ B we formulate a general hypothesis about the form of the asymptotics and confirm it in two cases: (1) ν=1 and the vectory has an arbitrary direction, (2)y is directed along a fixed axis and arbitrary ν. Here we use besides the saddle-point method, some arguments from scattering theory.
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Minlos, R.A., Zhizhina, E.A. Asymptotics of decay of correlations for lattice spin fields at high temperatures. I. The Ising model. J Stat Phys 84, 85–118 (1996). https://doi.org/10.1007/BF02179578
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DOI: https://doi.org/10.1007/BF02179578