Advertisement

Flow Equations and Main Result

  • Roland Bauerschmidt
  • David C. Brydges
  • Gordon Slade
Chapter
Part of the Lecture Notes in Mathematics book series (LNM, volume 2242)

Abstract

We analyse the perturbative renormalisation group flow derived in the previous chapter. When nonperturbative effects are ignored, we show how this analysis leads to a logarithmic correction to mean-field scaling for the 4-dimensional hierarchical susceptibility. Nonperturbative effects however cannot be ignored, and we state the extension of the results for the perturbative flow to its nonperturbative version and use this extension to prove the main results for the |φ|4 model. The analysis of the nonperturbative effects is carried out in subsequent chapters. The notion of infrared asymptotic freedom is discussed.

Keywords

Renormalisation group flow equations Stable manifold Susceptibility Infrared asymptotic freedom 

References

  1. 64.
    N.G. de Bruijn, Asymptotic Methods in Analysis, 3rd edn. (North Holland, Amsterdam, 1981)zbMATHGoogle Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  • Roland Bauerschmidt
    • 1
  • David C. Brydges
    • 2
  • Gordon Slade
    • 2
  1. 1.Department of Pure Mathematics and Mathematical StatisticsUniversity of CambridgeCambridgeUK
  2. 2.Department of MathematicsThe University of British ColumbiaVancouverCanada

Personalised recommendations