Communications in Mathematical Physics

, Volume 77, Issue 1, pp 31–64 | Cite as

A rigorous block spin approach to massless lattice theories

  • K. Gawedzki
  • A. Kupiainen
Article
Received:

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.

Keywords

Neural Network Free Energy Energy Density Nonlinear Dynamics Renormalization Group 
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Copyright information

© Springer-Verlag 1980

Authors and Affiliations

  • K. Gawedzki
    • 1
  • A. Kupiainen
    • 1
  1. 1.Lyman Laboratory of PhysicsHarvard UniversityCambridgeUSA

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