TY  - JOUR
A1  - Eichelsbacher, Peter
A1  - Martschink, Bastian
T1  - Rates of Convergence in the Blume–Emery–Griffiths Model
T2  - J Stat Phys (Journal of Statistical Physics)
N2  - 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.
KW  - Stein’s method
KW  - Exchangeable pairs
KW  - Blume–Emery–Griffith model
KW  - Second-order phase transition
KW  - First-order phase transition
KW  - Tricritical point
KW  - Blume–Capel model
Y1  - 2014
UR  - https://pub.h-brs.de/frontdoor/index/index/docId/1304
SN  - 0022-4715
N1  - The authors have been supported by Deutsche Forschungsgemeinschaft via SFB/TR 12.
VL  - 154
IS  - 6
SP  - 1483
EP  - 1507
PB  - Springer US
ER  -