Fluctuations of the Magnetization in the Block Potts Model
J. Jalowy, M. Löwe, H. Sambale, Journal of Statistical Physics 187 (2022).
Download
No fulltext has been uploaded.
Journal Article
| Published
| English
Author
Jalowy, Jonas;
Löwe, Matthias;
Sambale, Holger
Abstract
<jats:title>Abstract</jats:title><jats:p>In this note we study the block spin mean-field Potts model, in which the spins are divided into <jats:italic>s</jats:italic> blocks and can take <jats:inline-formula><jats:alternatives><jats:tex-math>$$q\ge 2$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
<mml:mrow>
<mml:mi>q</mml:mi>
<mml:mo>≥</mml:mo>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:math></jats:alternatives></jats:inline-formula> 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.</jats:p>
Publishing Year
Journal Title
Journal of Statistical Physics
Volume
187
Issue
1
Article Number
3
LibreCat-ID
Cite this
Jalowy J, Löwe M, Sambale H. Fluctuations of the Magnetization in the Block Potts Model. Journal of Statistical Physics. 2022;187(1). doi:10.1007/s10955-022-02889-4
Jalowy, J., Löwe, M., & Sambale, H. (2022). Fluctuations of the Magnetization in the Block Potts Model. Journal of Statistical Physics, 187(1), Article 3. https://doi.org/10.1007/s10955-022-02889-4
@article{Jalowy_Löwe_Sambale_2022, title={Fluctuations of the Magnetization in the Block Potts Model}, volume={187}, DOI={10.1007/s10955-022-02889-4}, number={13}, journal={Journal of Statistical Physics}, publisher={Springer Science and Business Media LLC}, author={Jalowy, Jonas and Löwe, Matthias and Sambale, Holger}, year={2022} }
Jalowy, Jonas, Matthias Löwe, and Holger Sambale. “Fluctuations of the Magnetization in the Block Potts Model.” Journal of Statistical Physics 187, no. 1 (2022). https://doi.org/10.1007/s10955-022-02889-4.
J. Jalowy, M. Löwe, and H. Sambale, “Fluctuations of the Magnetization in the Block Potts Model,” Journal of Statistical Physics, vol. 187, no. 1, Art. no. 3, 2022, doi: 10.1007/s10955-022-02889-4.
Jalowy, Jonas, et al. “Fluctuations of the Magnetization in the Block Potts Model.” Journal of Statistical Physics, vol. 187, no. 1, 3, Springer Science and Business Media LLC, 2022, doi:10.1007/s10955-022-02889-4.