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The magnetization-energy scaling limit in high dimension

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Abstract

In the single-phase region (including the critical point) of a nearest-neighbor Ising ferromagnet with zero external field, the block magnetization and energy within the infinite-volume system are, asymptotically for large block size, independent Gaussian variables when the dimensiond exceeds four. For other models, including ones with long-range interactions, a sufficient condition for such triviality of the scaling limit is finiteness of the “bubble quantity”.

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Authors and Affiliations

  1. Faculté des Sciences, Université de Mons, 7000, Mons, Belgium

    Jo/:el De Coninck

  2. Courant Institute of Mathematical Sciences, 10012, New York, New York

    Charles M. Newman

Authors
  1. Jo/:el De Coninck
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  2. Charles M. Newman
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On leave from the University of Arizona, Tucson, Arizona 85721.

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De Coninck, J., Newman, C.M. The magnetization-energy scaling limit in high dimension. J Stat Phys 59, 1451–1467 (1990). https://doi.org/10.1007/BF01334759

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