A Renormalisation Group Method. III. Perturbative Analysis

Roland Bauerschmidt, David C. Brydges, Gordon Slade

Research output: Contribution to journalArticlepeer-review


This paper is the third in a series devoted to the development of a rigorous renormalisation group method for lattice field theories involving boson fields, fermion fields, or both. In this paper, we motivate and present a general approach towards second-order perturbative renormalisation, and apply it to a specific supersymmetric field theory which represents the continuous-time weakly self-avoiding walk on Our focus is on the critical dimension $$d=4$$d=4. The results include the derivation of the perturbative flow of the coupling constants, with accompanying estimates on the coefficients in the flow. These are essential results for subsequent application to the 4-dimensional weakly self-avoiding walk, including a proof of existence of logarithmic corrections to their critical scaling. With minor modifications, our results also apply to the 4-dimensional $$n$$n-component spin model.

Original languageEnglish (US)
Pages (from-to)492-529
Number of pages38
JournalJournal of Statistical Physics
Issue number3
StatePublished - May 1 2015


  • Perturbation theory
  • Renormalisation group
  • Self-avoiding walk

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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