Flow Equations and Main Result

Roland Bauerschmidt, David C. Brydges, Gordon Slade

Research output: Chapter in Book/Report/Conference proceedingChapter


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.

Original languageEnglish (US)
Title of host publicationLecture Notes in Mathematics
PublisherSpringer Verlag
Number of pages16
StatePublished - 2019

Publication series

NameLecture Notes in Mathematics
ISSN (Print)0075-8434
ISSN (Electronic)1617-9692


  • Infrared asymptotic freedom
  • Renormalisation group flow equations
  • Stable manifold
  • Susceptibility

ASJC Scopus subject areas

  • Algebra and Number Theory


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