Asymptotics of Mean-Field O(N) Models

Kay Kirkpatrick, Tayyab Nawaz

Research output: Contribution to journalArticlepeer-review

Abstract

We study mean-field classical N-vector models, for integers N≥ 2. We use the theory of large deviations and Stein’s method to study the total spin and its typical behavior, specifically obtaining non-normal limit theorems at the critical temperatures and central limit theorems away from criticality. Important special cases of these models are the XY (N= 2) model of superconductors, the Heisenberg (N= 3) model [previously studied in Kirkpatrick and Meckes (J Stat Phys 152:54–92, 2013) but with a correction to the critical distribution here], and the Toy (N= 4) model of the Higgs sector in particle physics.

Original languageEnglish (US)
Pages (from-to)1114-1140
Number of pages27
JournalJournal of Statistical Physics
Volume165
Issue number6
DOIs
StatePublished - Dec 1 2016

Keywords

  • Limit theorem
  • Mean-field
  • Phase transition
  • Rate function
  • Total spin

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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