Epsilon expansion for multicritical fixed points and exact renormalisation group equations

J. O'Dwyer, H. Osborn

Research output: Contribution to journalArticlepeer-review


The Polchinski version of the exact renormalisation group equations is applied to multicritical fixed points, which are present for dimensions between two and four, for scalar theories using both the local potential approximation and its extension, the derivative expansion. The results are compared with the epsilon expansion by showing that the nonlinear differential equations may be linearised at each multicritical point and the epsilon expansion treated as a perturbative expansion. The results for critical exponents are compared with corresponding epsilon expansion results from standard perturbation theory. The results provide a test for the validity of the local potential approximation and also the derivative expansion. An alternative truncation of the exact RG equation leads to equations which are similar to those found in the derivative expansion but which gives correct results for critical exponents to order ε and also for the field anomalous dimension to order ε2. An exact marginal operator for the full RG equations is also constructed.

Original languageEnglish (US)
Pages (from-to)1859-1898
Number of pages40
JournalAnnals of Physics
Issue number8
StatePublished - Aug 2008
Externally publishedYes


  • Epsilon expansion
  • Exact renormalisation group
  • Multicritical points

ASJC Scopus subject areas

  • General Physics and Astronomy


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