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Critical Behavior of Mean-Field XY and Related Models

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Stochastic Analysis and Related Topics

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

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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.

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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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Authors and Affiliations

  1. Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 W. Green Street, Urbana, IL, 61801, USA

    Kay Kirkpatrick & Tayyab Nawaz

  2. Department of Mathematics, COMSATS Institute of Information and Technology, Park Road, Islamabad, 45550, Pakistan

    Tayyab Nawaz

Authors
  1. Kay Kirkpatrick
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  2. Tayyab Nawaz
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Correspondence to Tayyab Nawaz .

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Editors and Affiliations

  1. Department of Mathematics, University of Connecticut, Storrs, Connecticut, USA

    Fabrice Baudoin

  2. Department of Mathematics, Purdue University, West Lafayette, Indiana, USA

    Jonathon Peterson

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Kirkpatrick, K., Nawaz, T. (2017). Critical Behavior of Mean-Field XY and Related Models. In: Baudoin, F., Peterson, J. (eds) Stochastic Analysis and Related Topics. Progress in Probability, vol 72. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-59671-6_10

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