The statistics of Curie-Weiss models

Richard S. Ellis, Charles M. Newman

Research output: Contribution to journalArticlepeer-review


Let Sn denote the random total magnetization of an n-site Curie-Weiss model, a collection of n (spin) random variables with an equal interaction of strength 1/n between each pair of spins. The asymptotic behavior for large n of the probability distribution of Sn is analyzed and related to the well-known (mean-field) thermodynamic properties of these models. One particular result is that at a type-k critical point (Sn-nm)/n1-1/2k has a limiting distribution with density proportional to exp[-λs2k/(2k)!], where m is the mean magnetization per site and A is a positive critical parameter with a universal upper bound. Another result describes the asymptotic behavior relevant to metastability.

Original languageEnglish (US)
Pages (from-to)149-161
Number of pages13
JournalJournal of Statistical Physics
Issue number2
StatePublished - Aug 1978


  • Block spin
  • Curie-Weiss
  • mean-field
  • renormalization group

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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