In the framework of the renormalization group and the e{open}-expansion, we propose expressions for the β-function and anomalous dimensions in terms of renormalized one-irreducible functions. These expressions are convenient for numerical calculations. We choose the renormalization scheme in which the quantities calculated using R operations are represented by integrals that do not contain singularities in e{open}. We develop a completely automated calculation system starting from constructing diagrams, determining relevant subgraphs, combinatorial coefficients, etc., up to determining critical exponents. As an example, we calculate the critical exponents of the φ3 model in the order e{open}4.

Original languageEnglish
Pages (from-to)1450-1459
Number of pages10
JournalTheoretical and Mathematical Physics
Volume169
Issue number1
DOIs
StatePublished - 1 Oct 2011

    Research areas

  • critical exponents, e{open}-expansion, multiloop diagrams, renormalization group

    Scopus subject areas

  • Mathematical Physics
  • Statistical and Nonlinear Physics

ID: 36313120