Geodesic
Translation Invariance of the~periodic Gibbs measures for the~Potts model on the~Cayley tree
Teoretičeskaâ i matematičeskaâ fizika, Tome 199 (2019) no. 2, pp. 291-301

Voir la notice de l'article provenant de la source Math-Net.Ru

We study the Potts model with a zero external field on the Cayley tree. For the antiferromagnetic Potts model with $q$ states on a second-order Cayley tree and for the ferromagnetic Potts model with $q$ states on a $k$th-order Cayley tree, we show that all periodic Gibbs measures are translation-invariant for all parameter values.
Keywords: Cayley tree, Potts model, Gibbs measure, periodic measure, translation-invariant measure.
Mots-clés : configuration 
@article{TMF_2019_199_2_a8,
     author = {R. M. Khakimov and M. T. Makhammadaliev},
     title = {Translation {Invariance} of the~periodic {Gibbs} measures for {the~Potts} model on {the~Cayley} tree},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {291--301},
     publisher = {mathdoc},
     volume = {199},
     number = {2},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2019_199_2_a8/}
}
TY  - JOUR
AU  - R. M. Khakimov
AU  - M. T. Makhammadaliev
TI  - Translation Invariance of the~periodic Gibbs measures for the~Potts model on the~Cayley tree
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2019
SP  - 291
EP  - 301
VL  - 199
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TMF_2019_199_2_a8/
LA  - ru
ID  - TMF_2019_199_2_a8
ER  - 
%0 Journal Article
%A R. M. Khakimov
%A M. T. Makhammadaliev
%T Translation Invariance of the~periodic Gibbs measures for the~Potts model on the~Cayley tree
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2019
%P 291-301
%V 199
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TMF_2019_199_2_a8/
%G ru
%F TMF_2019_199_2_a8
R. M. Khakimov; M. T. Makhammadaliev. Translation Invariance of the~periodic Gibbs measures for the~Potts model on the~Cayley tree. Teoretičeskaâ i matematičeskaâ fizika, Tome 199 (2019) no. 2, pp. 291-301. http://geodesic.mathdoc.fr/item/TMF_2019_199_2_a8/