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A rigorous block spin approach to massless lattice theories

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Abstract

The renormalization group technique is used to study rigorously the λ(∇φ)4 perturbation of the massless lattice field φ in dimensionsd≧2. Asymptoticity of the perturbation expansion in powers of λ is established for the free energy density. This is achieved by using Kadanoff's block spin transformation successively to integrate out high momentum degrees of freedom and by applying ideas previously used by Gallavotti and Balaban in the context of the ultraviolet problems. The method works for arbitrary semibounded polynomials in ∇φ and △φ.

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Author notes

  1. A. Kupiainen

    Present address: Research Institute for Theoretical Physics, Helsinki University, SF-00170, Helsinki 17, Finland

Authors and Affiliations

  1. Lyman Laboratory of Physics, Harvard University, 02138, Cambridge, Massachusetts, USA

    K. Gawedzki & A. Kupiainen

Authors
  1. K. Gawedzki
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  2. A. Kupiainen
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Additional information

Communicated by A. Jaffe

Supported in part by the National Science Foundation under Grant No. PHY 79-16812

On leave from Department of Mathematical Methods of Physics, University, PL-00-682 Warsaw, Poland

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Gawedzki, K., Kupiainen, A. A rigorous block spin approach to massless lattice theories. Commun.Math. Phys. 77, 31–64 (1980). https://doi.org/10.1007/BF01205038

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  • DOI: https://doi.org/10.1007/BF01205038

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