The statistics of Curie-Weiss models

Richard S. Ellis, Charles M. Newman

Research output: Contribution to journalArticle

Abstract

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[-λs 2k/(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
Volume19
Issue number2
DOIs
StatePublished - Aug 1978

Fingerprint

Magnetization
Asymptotic Behavior
statistics
Statistics
Metastability
magnetization
random variables
Thermodynamic Properties
Limiting Distribution
metastable state
Mean Field
Critical point
critical point
Probability Distribution
thermodynamic properties
Random variable
Directly proportional
Upper bound
Denote
Interaction

Keywords

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

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Physics and Astronomy(all)
  • Mathematical Physics

Cite this

The statistics of Curie-Weiss models. / Ellis, Richard S.; Newman, Charles M.

In: Journal of Statistical Physics, Vol. 19, No. 2, 08.1978, p. 149-161.

Research output: Contribution to journalArticle

Ellis, Richard S. ; Newman, Charles M. / The statistics of Curie-Weiss models. In: Journal of Statistical Physics. 1978 ; Vol. 19, No. 2. pp. 149-161.
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