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Normal fluctuations and the FKG inequalities

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Abstract

In a translation invariant pure phase of a ferromagnet, finite susceptibility and the FKG inequalities together imply convergence of the block spin scaling limit to the infinite temperature Gaussian fixed point. This result is presented in a rather general probabilistic context and is applicable to infinite cluster density fluctuations in percolation models and to boson field fluctuations in (Euclidean) Yukawa quantum field theory models as well as to magnetization fluctuations in Ising models.

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Authors and Affiliations

  1. Department of Mathematics, University of Arizona, 85721, Tucson, AZ, USA

    C. M. Newman

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  1. C. M. Newman
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Communicated by E. Lieb

Alfred P. Sloan Research Fellow, on leave from Indiana University. Research supported in part by National Science Foundation Grant MCS 77-20683 and by the U.S.-Israel Binational Science Foundation

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Newman, C.M. Normal fluctuations and the FKG inequalities. Commun.Math. Phys. 74, 119–128 (1980). https://doi.org/10.1007/BF01197754

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  • DOI: https://doi.org/10.1007/BF01197754

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