Fluctuations of the magnetization in the Block Potts Model

Jalowy J, Loewe M, Sambale H (2022)
Journal of Statistical Physics 187(1): 3.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Jalowy, Jonas; Loewe, Matthias; Sambale, HolgerUniBi
Abstract / Bemerkung
In this note we study the block spin mean-field Potts model, in which the spins are divided into s blocks and can take q >= 2 different values (colors). Each block is allowed to contain a different proportion of vertices and behaves itself like a mean-field Ising/Potts model which also interacts with other blocks according to different temperatures. Of particular interest is the behavior of the magnetization, which counts the number of colors appearing in the distinct blocks. We prove central limit theorems for the magnetization in the generalized high-temperature regime and provide a moderate deviation principle for its fluctuations on lower scalings. More precisely, the magnetization concentrates around the uniform vector of all colors with an explicit, but singular, Gaussian distribution. In order to remove the singular component, we will also consider a rotated magnetization, which enables us to compare our results to various related models.
Stichworte
Potts model; Block spin model; Central limit theorem; Moderate; deviations
Erscheinungsjahr
2022
Zeitschriftentitel
Journal of Statistical Physics
Band
187
Ausgabe
1
Art.-Nr.
3
ISSN
0022-4715
eISSN
1572-9613
Page URI
https://pub.uni-bielefeld.de/record/2961632

Zitieren

Jalowy J, Loewe M, Sambale H. Fluctuations of the magnetization in the Block Potts Model. Journal of Statistical Physics . 2022;187(1): 3.
Jalowy, J., Loewe, M., & Sambale, H. (2022). Fluctuations of the magnetization in the Block Potts Model. Journal of Statistical Physics , 187(1), 3. https://doi.org/10.1007/s10955-022-02889-4
Jalowy, J., Loewe, M., and Sambale, H. (2022). Fluctuations of the magnetization in the Block Potts Model. Journal of Statistical Physics 187:3.
Jalowy, J., Loewe, M., & Sambale, H., 2022. Fluctuations of the magnetization in the Block Potts Model. Journal of Statistical Physics , 187(1): 3.
J. Jalowy, M. Loewe, and H. Sambale, “Fluctuations of the magnetization in the Block Potts Model”, Journal of Statistical Physics , vol. 187, 2022, : 3.
Jalowy, J., Loewe, M., Sambale, H.: Fluctuations of the magnetization in the Block Potts Model. Journal of Statistical Physics . 187, : 3 (2022).
Jalowy, Jonas, Loewe, Matthias, and Sambale, Holger. “Fluctuations of the magnetization in the Block Potts Model”. Journal of Statistical Physics 187.1 (2022): 3.

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