Periodic Gibbs measures for the Potts model in translation-invariant and periodic external fields on the Cayley tree

We study the Potts model in translation-invariant and periodic external fields on the Cayley tree of order . For the Potts model in a translation-invariant external field for , the nonuniqueness of the translation-invariant and periodic Gibbs measure is shown. It is proved that for the Potts model i...

Full description

Saved in:
Bibliographic Details
Published in:Theoretical and mathematical physics 2022, Vol.210 (1), p.135-153
Main Authors: Rozikov, U. A., Rakhmatullaev, M. M., Khakimov, R. M.
Format: Article
Language:English
Subjects:
14/34
639/766/189
639/766/530
639/766/747
Applications of Mathematics
Invariants
Mathematical and Computational Physics
Physics
Physics and Astronomy
Theoretical
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We study the Potts model in translation-invariant and periodic external fields on the Cayley tree of order . For the Potts model in a translation-invariant external field for , the nonuniqueness of the translation-invariant and periodic Gibbs measure is shown. It is proved that for the Potts model in an external field that is not translation-invariant, translation-invariant Gibbs measures do not exist on the Cayley tree of order . Periodic Gibbs measures are also studied for the Potts model in a periodic external field. We prove that under certain conditions, the number of such measures can be at least three.
ISSN:0040-5779
1573-9333
DOI:10.1134/S004057792201010X