Mayer expansions and the Hamilton-Jacobi equation

D. C. Brydges, T. Kennedy

Research output: Contribution to journalArticlepeer-review

85 Scopus citations


We review the derivation of Wilson's differential equation in (infinitely) many variables, which describes the infinitesimal change in an effective potential of a statistical mechanical model or quantum field theory when an infinitesimal "integration out" is performed. We show that this equation can be solved for short times by a very elementary method when the initial data are bounded and analytic. The resulting series solutions are generalizations of the Mayer expansion in statistical mechanics. The differential equation approach gives a remarkable identity for "connected parts" and precise estimates which include criteria for convergence of iterated Mayer expansions. Applications include the Yukawa gas in two dimensions past the Β=4 π threshold and another derivation of some earlier results of Göpfert and Mack.

Original languageEnglish (US)
Pages (from-to)19-49
Number of pages31
JournalJournal of Statistical Physics
Issue number1-2
StatePublished - Jul 1987


  • Multiscale Mayer expansions
  • renormalization group
  • tree graph identities

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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