Abstract
We prove that for low temperaturesT the spin-spin correlation function of the two-dimensional classicalSO(n)-symmetric Ising ferromagnet decays faster than |x|−constT providedn≧2. We also discuss a nearest neighbor continuous spin model, with spins restricted to a finite interval, where we show that the spin-spin correlation function decays exponentially in any number of dimensions.
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Communicated by A. Jaffe
Work supported in part by NSF, Grant PHY76-17191
A Sloan Fellow
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McBryan, O.A., Spencer, T. On the decay of correlations inSO(n)-symmetric ferromagnets. Commun.Math. Phys. 53, 299–302 (1977). https://doi.org/10.1007/BF01609854
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DOI: https://doi.org/10.1007/BF01609854