Critical Behavior of Mean-Field XY and Related Models

Conference paper
Part of the Progress in Probability book series (PRPR, volume 72)

Abstract

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.

Keywords

Mean-field Free energy Density function Gibbs measure 

Notes

Acknowledgements

Both authors partially supported by NSF CAREER award DMS-1254791, and NSF grant 0932078 000 while in residence at MSRI during Fall 2015.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of Illinois at Urbana-ChampaignUrbanaUSA
  2. 2.Department of MathematicsCOMSATS Institute of Information and TechnologyIslamabadPakistan

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