Asymptotics of decay of correlations for lattice spin fields at high temperatures. I. The Ising model |
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Authors: | R. A. Minlos E. A. Zhizhina |
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Affiliation: | (1) Institute for Problems of Information Transmission, Russian Academy of Science, 101447 Moscow, Russia |
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Abstract: | We find the asymptotic decrease of correlations < A +y, B>,y Zv+1, |y|![rarr](/content/7135l14x2852j464/xxlarge8594.gif) , in the Ising model at high temperatures. For the case when monomials A and B both are odd, using the saddle-point method, we find the asymptotics of the correlations for any dimension . For even monomials A, B we formulate a general hypothesis about the form of the asymptotics and confirm it in two cases: (1) =1 and the vectory has an arbitrary direction, (2)y is directed along a fixed axis and arbitrary . Here we use besides the saddle-point method, some arguments from scattering theory. |
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Keywords: | Ising model Markov chain transfer matrix Friedrichs model saddle-point method scattering theory T-matrix |
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