Critical Behavior of Mean-Field XY and Related Models

Kay Kirkpatrick, Tayyab Nawaz

Research output: Chapter in Book/Report/Conference proceedingChapter


We discuss spin models on complete graphs in the mean-field (infinite-vertex) limit, especially the classical XY model, the Toy model of the Higgs sector, and related generalizations. We present a number of results coming from the theory of large deviations and Stein’s method, in particular, Cramér and Sanov-type results, limit theorems with rates of convergence, and phase transition behavior for these models.

Original languageEnglish (US)
Title of host publicationStochastic Analysis and Related Topics
Subtitle of host publicationA Festschrift in Honor of Rodrigo Bañuelos
EditorsFabrice Baudoin, Jonathon Peterson
Number of pages15
ISBN (Print)978-3-319-59670-9, 978-3-319-86676-5
StatePublished - 2017

Publication series

NameProgress in Probability
ISSN (Print)1050-6977
ISSN (Electronic)2297-0428


  • Density function
  • Free energy
  • Gibbs measure
  • Mean-field

ASJC Scopus subject areas

  • Statistics and Probability
  • Applied Mathematics
  • Mathematical Physics
  • Mathematics (miscellaneous)


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