Rigorous Renormalization Group and Large N

  • Krzysztof Gawedzki
  • Antti Kupiainen
Part of the NATO ASI Series book series (NSSB, volume 115)


In this lecture we discuss an attempt to obtain a rigorous control of the models of equilibrium statistical mechanics and Euclidean quantum field theory with the spins (fields) transforming under the fundamental representation of 0(N) for N large. Our approach is based on a renormalization group (RG) analysis, see [16]. The idea is to use the leading orders of the 1/N expansion to deduce a qualitative behaviour of the RG effective interactions, borrowing heavily on the existing heuristic arguments [17, 18];. and to perform a non-perturbative analysis of the corrections with the use of analyticity techniques developed by us [16]. The most interesting models for which our approach might be ultimately applicable i ncIude
  • critical point of \({({\overrightarrow \varphi ^2})^2}\)] in three dimensions with its non-canonical long distance behaviour,

  • 0(N) σ-model in two dimensions with conjectured mass generation and asymptotically free renormalizable continuum limit,

  • tricritical point of \({({{\vec \varphi }^2})^3}\)] in three dimensions with a presumed non-Gaussian short distance behaviour.


Renormalization Group Tricritical Point Block Spin Real Symmetric Matrice Renormal Ization Group Transformation 
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Copyright information

© Plenum Press, New York 1984

Authors and Affiliations

  • Krzysztof Gawedzki
    • 1
    • 3
  • Antti Kupiainen
    • 2
  1. 1.C. N. R. S., I. H. E. S.Bures-sur-YvetteFrance
  2. 2.Department of Technical PhysicsHelsinki University of TechnologyEspoo 15Finland
  3. 3.Department of Mathematical Methods of PhysicsWarsaw UniversityPoland

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