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Scaling limit of the energy variable for the two-dimensional Ising ferromagnet

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Abstract

The critical point limit law (scaling limit) of the suitably renormalized energy variable is explicitly calculated for the two-dimensional nearest-neighbour Ising cylinder with free edges. It is shown that the renormalization factor has to behave as (2M 2N lnN)1/2, where 2M denotes the number of rows and 2N the number of columns. By first taking the limitM→∞ and thenN→∞, the limit law is proven to be Gaussian.

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  1. Université de l'Etat Faculté des Sciences, B-7000, Mons, Belgium

    Joël De Coninck

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  1. Joël De Coninck
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Communicated by J. Fröhlich

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De Coninck, J. Scaling limit of the energy variable for the two-dimensional Ising ferromagnet. Commun.Math. Phys. 95, 53–59 (1984). https://doi.org/10.1007/BF01215755

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  • DOI: https://doi.org/10.1007/BF01215755

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