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Rates of Convergence in the Blume–Emery–Griffiths Model

  • We derive rates of convergence for limit theorems that reveal the intricate structure of the phase transitions in a mean-field version of the Blume–Emery–Griffith model. The theorems consist of scaling limits for the total spin. The model depends on the inverse temperature β and the interaction strength K. The rates of convergence results are obtained as (β,K) converges along appropriate sequences (βn,Kn) to points belonging to various subsets of the phase diagram which include a curve of second-order points and a tricritical point. We apply Stein’s method for normal and non-normal approximation avoiding the use of transforms and supplying bounds, such as those of Berry–Esseen quality, on approximation error.

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Document Type:Article
Author:Peter Eichelsbacher, Bastian Martschink
Parent Title (English):J Stat Phys (Journal of Statistical Physics)
First Page:1483
Last Page:1507
Publisher:Springer US
Date of first publication:2014/02/19
The authors have been supported by Deutsche Forschungsgemeinschaft via SFB/TR 12.
Tag:Blume–Capel model; Blume–Emery–Griffith model; Exchangeable pairs; First-order phase transition; Second-order phase transition; Stein’s method; Tricritical point
Departments, institutes and facilities:Fachbereich Elektrotechnik, Maschinenbau, Technikjournalismus
Dewey Decimal Classification (DDC):5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
Entry in this database:2015/04/02