Large deviations, a phase transition, and logarithmic Sobolev inequalities in the block spin Potts model

Knoepfel H, Loewe M, Sambale H (2021)
Electronic Communications in Probability 26: 29.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
Download
Es wurden keine Dateien hochgeladen. Nur Publikationsnachweis!
Autor*in
Knoepfel, Holger; Loewe, Matthias; Sambale, HolgerUniBi
Abstract / Bemerkung
We introduce and analyze a generalization of the blocks spin Ising (Curie-Weiss) models that were discussed in a number of recent articles. In these block spin models each spin in one of s blocks can take one of a finite number of q >= 3 values or colors, hence the name block spin Potts model. We prove a large deviation principle for the percentage of spins of a certain color in a certain block. These values are represented in an s X q matrix. We show that for uniform block sizes there is a phase transition. In some regime the only equilibrium is the uniform distribution of all colors in all blocks, while in other parameter regimes there is one predominant color, and this is the same color with the same frequency for all blocks. Finally, we establish log-Sobolev-type inequalities for the block spin Potts model.
Stichworte
block spin Potts model; large deviation principle; logarithmic Sobolev; inequality; phase transition
Erscheinungsjahr
2021
Zeitschriftentitel
Electronic Communications in Probability
Band
26
Art.-Nr.
29
ISSN
1083-589X
Page URI
https://pub.uni-bielefeld.de/record/2955703

Zitieren

Knoepfel H, Loewe M, Sambale H. Large deviations, a phase transition, and logarithmic Sobolev inequalities in the block spin Potts model. Electronic Communications in Probability. 2021;26: 29.
Knoepfel, H., Loewe, M., & Sambale, H. (2021). Large deviations, a phase transition, and logarithmic Sobolev inequalities in the block spin Potts model. Electronic Communications in Probability, 26, 29. https://doi.org/10.1214/21-ECP397
Knoepfel, H., Loewe, M., and Sambale, H. (2021). Large deviations, a phase transition, and logarithmic Sobolev inequalities in the block spin Potts model. Electronic Communications in Probability 26:29.
Knoepfel, H., Loewe, M., & Sambale, H., 2021. Large deviations, a phase transition, and logarithmic Sobolev inequalities in the block spin Potts model. Electronic Communications in Probability, 26: 29.
H. Knoepfel, M. Loewe, and H. Sambale, “Large deviations, a phase transition, and logarithmic Sobolev inequalities in the block spin Potts model”, Electronic Communications in Probability, vol. 26, 2021, : 29.
Knoepfel, H., Loewe, M., Sambale, H.: Large deviations, a phase transition, and logarithmic Sobolev inequalities in the block spin Potts model. Electronic Communications in Probability. 26, : 29 (2021).
Knoepfel, Holger, Loewe, Matthias, and Sambale, Holger. “Large deviations, a phase transition, and logarithmic Sobolev inequalities in the block spin Potts model”. Electronic Communications in Probability 26 (2021): 29.

Export

Markieren/ Markierung löschen
Markierte Publikationen

Open Data PUB

Web of Science

Dieser Datensatz im Web of Science®

Suchen in

Google Scholar