---
_id: '59186'
abstract:
- lang: eng
  text: "<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\">\r\n
    \                 <mml:mrow>\r\n                    <mml:mi>q</mml:mi>\r\n                    <mml:mo>≥</mml:mo>\r\n
    \                   <mml:mn>2</mml:mn>\r\n                  </mml:mrow>\r\n                </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>"
article_number: '3'
author:
- first_name: Jonas
  full_name: Jalowy, Jonas
  id: '113768'
  last_name: Jalowy
  orcid: 0000-0001-9624-2685
- first_name: Matthias
  full_name: Löwe, Matthias
  last_name: Löwe
- first_name: Holger
  full_name: Sambale, Holger
  last_name: Sambale
citation:
  ama: Jalowy J, Löwe M, Sambale H. Fluctuations of the Magnetization in the Block
    Potts Model. <i>Journal of Statistical Physics</i>. 2022;187(1). doi:<a href="https://doi.org/10.1007/s10955-022-02889-4">10.1007/s10955-022-02889-4</a>
  apa: Jalowy, J., Löwe, M., &#38; Sambale, H. (2022). Fluctuations of the Magnetization
    in the Block Potts Model. <i>Journal of Statistical Physics</i>, <i>187</i>(1),
    Article 3. <a href="https://doi.org/10.1007/s10955-022-02889-4">https://doi.org/10.1007/s10955-022-02889-4</a>
  bibtex: '@article{Jalowy_Löwe_Sambale_2022, title={Fluctuations of the Magnetization
    in the Block Potts Model}, volume={187}, DOI={<a href="https://doi.org/10.1007/s10955-022-02889-4">10.1007/s10955-022-02889-4</a>},
    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} }'
  chicago: Jalowy, Jonas, Matthias Löwe, and Holger Sambale. “Fluctuations of the
    Magnetization in the Block Potts Model.” <i>Journal of Statistical Physics</i>
    187, no. 1 (2022). <a href="https://doi.org/10.1007/s10955-022-02889-4">https://doi.org/10.1007/s10955-022-02889-4</a>.
  ieee: 'J. Jalowy, M. Löwe, and H. Sambale, “Fluctuations of the Magnetization in
    the Block Potts Model,” <i>Journal of Statistical Physics</i>, vol. 187, no. 1,
    Art. no. 3, 2022, doi: <a href="https://doi.org/10.1007/s10955-022-02889-4">10.1007/s10955-022-02889-4</a>.'
  mla: Jalowy, Jonas, et al. “Fluctuations of the Magnetization in the Block Potts
    Model.” <i>Journal of Statistical Physics</i>, vol. 187, no. 1, 3, Springer Science
    and Business Media LLC, 2022, doi:<a href="https://doi.org/10.1007/s10955-022-02889-4">10.1007/s10955-022-02889-4</a>.
  short: J. Jalowy, M. Löwe, H. Sambale, Journal of Statistical Physics 187 (2022).
date_created: 2025-03-31T07:14:09Z
date_updated: 2025-04-23T14:38:45Z
doi: 10.1007/s10955-022-02889-4
intvolume: '       187'
issue: '1'
language:
- iso: eng
publication: Journal of Statistical Physics
publication_identifier:
  issn:
  - 0022-4715
  - 1572-9613
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: Fluctuations of the Magnetization in the Block Potts Model
type: journal_article
user_id: '113768'
volume: 187
year: '2022'
...