Critical Behavior of Mean-Field XY and Related Models

Kay Kirkpatrick, Tayyab Nawaz

Research output: Chapter in Book/Report/Conference proceedingChapter

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.
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
PublisherBirkhäuser Basel
Chapter10
Pages207-221
ISBN (Print)978-3-319-59670-9, 978-3-319-86676-5
DOIs
StatePublished - Sep 27 2017

Publication series

NameProgress in Probability
Volume72
ISSN (Print)1050-6977
ISSN (Electronic)2297-0428

Fingerprint

apexes
sectors
theorems
deviation

Keywords

  • mean-field
  • free energy
  • density function
  • Gibbs measure

Cite this

Kirkpatrick, K., & Nawaz, T. (2017). Critical Behavior of Mean-Field XY and Related Models. In F. Baudoin, & J. Peterson (Eds.), Stochastic Analysis and Related Topics: A Festschrift in Honor of Rodrigo Bañuelos (pp. 207-221). (Progress in Probability; Vol. 72). Birkhäuser Basel. https://doi.org/10.1007/978-3-319-59671-6_10

Critical Behavior of Mean-Field XY and Related Models. / Kirkpatrick, Kay; Nawaz, Tayyab.

Stochastic Analysis and Related Topics: A Festschrift in Honor of Rodrigo Bañuelos. ed. / Fabrice Baudoin; Jonathon Peterson. Birkhäuser Basel, 2017. p. 207-221 (Progress in Probability; Vol. 72).

Research output: Chapter in Book/Report/Conference proceedingChapter

Kirkpatrick, K & Nawaz, T 2017, Critical Behavior of Mean-Field XY and Related Models. in F Baudoin & J Peterson (eds), Stochastic Analysis and Related Topics: A Festschrift in Honor of Rodrigo Bañuelos. Progress in Probability, vol. 72, Birkhäuser Basel, pp. 207-221. https://doi.org/10.1007/978-3-319-59671-6_10
Kirkpatrick K, Nawaz T. Critical Behavior of Mean-Field XY and Related Models. In Baudoin F, Peterson J, editors, Stochastic Analysis and Related Topics: A Festschrift in Honor of Rodrigo Bañuelos. Birkhäuser Basel. 2017. p. 207-221. (Progress in Probability). https://doi.org/10.1007/978-3-319-59671-6_10
Kirkpatrick, Kay ; Nawaz, Tayyab. / Critical Behavior of Mean-Field XY and Related Models. Stochastic Analysis and Related Topics: A Festschrift in Honor of Rodrigo Bañuelos. editor / Fabrice Baudoin ; Jonathon Peterson. Birkhäuser Basel, 2017. pp. 207-221 (Progress in Probability).
@inbook{dffeff249b134a87b034826cc2a62514,
title = "Critical Behavior of Mean-Field XY and Related Models",
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, Cram{\'e}r 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",
author = "Kay Kirkpatrick and Tayyab Nawaz",
year = "2017",
month = "9",
day = "27",
doi = "10.1007/978-3-319-59671-6_10",
language = "English (US)",
isbn = "978-3-319-59670-9",
series = "Progress in Probability",
publisher = "Birkh{\"a}user Basel",
pages = "207--221",
editor = "Fabrice Baudoin and Jonathon Peterson",
booktitle = "Stochastic Analysis and Related Topics",

}

TY - CHAP

T1 - Critical Behavior of Mean-Field XY and Related Models

AU - Kirkpatrick, Kay

AU - Nawaz, Tayyab

PY - 2017/9/27

Y1 - 2017/9/27

N2 - 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.

AB - 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.

KW - mean-field

KW - free energy

KW - density function

KW - Gibbs measure

U2 - 10.1007/978-3-319-59671-6_10

DO - 10.1007/978-3-319-59671-6_10

M3 - Chapter

SN - 978-3-319-59670-9

SN - 978-3-319-86676-5

T3 - Progress in Probability

SP - 207

EP - 221

BT - Stochastic Analysis and Related Topics

A2 - Baudoin, Fabrice

A2 - Peterson, Jonathon

PB - Birkhäuser Basel

ER -