Geodesic
A~$p$-adic generalized Gibbs measure for the~ Ising model on a~Cayley tree
Teoretičeskaâ i matematičeskaâ fizika, Tome 201 (2019) no. 1, pp. 126-136

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

We consider a $p$-adic Ising model on the Cayley tree of order $k\ge2$. We completely describe all $p$-adic translation-invariant generalized Gibbs measures for $k=3$. Moreover, we show the existence of a phase transition for the $p$-adic Ising model for any $k\ge3$ if $p\equiv1\!\pmod4$.
Keywords: $p$-adic number, Ising model, Gibbs measure
Mots-clés : phase transition. 
@article{TMF_2019_201_1_a8,
     author = {M. M. Rahmatullaev and O. N. Khakimov and A. M. Tukhtaboev},
     title = {A~$p$-adic generalized {Gibbs} measure for the~ {Ising} model on {a~Cayley} tree},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {126--136},
     publisher = {mathdoc},
     volume = {201},
     number = {1},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2019_201_1_a8/}
}
TY  - JOUR
AU  - M. M. Rahmatullaev
AU  - O. N. Khakimov
AU  - A. M. Tukhtaboev
TI  - A~$p$-adic generalized Gibbs measure for the~ Ising model on a~Cayley tree
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2019
SP  - 126
EP  - 136
VL  - 201
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TMF_2019_201_1_a8/
LA  - ru
ID  - TMF_2019_201_1_a8
ER  - 
%0 Journal Article
%A M. M. Rahmatullaev
%A O. N. Khakimov
%A A. M. Tukhtaboev
%T A~$p$-adic generalized Gibbs measure for the~ Ising model on a~Cayley tree
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2019
%P 126-136
%V 201
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TMF_2019_201_1_a8/
%G ru
%F TMF_2019_201_1_a8
M. M. Rahmatullaev; O. N. Khakimov; A. M. Tukhtaboev. A~$p$-adic generalized Gibbs measure for the~ Ising model on a~Cayley tree. Teoretičeskaâ i matematičeskaâ fizika, Tome 201 (2019) no. 1, pp. 126-136. http://geodesic.mathdoc.fr/item/TMF_2019_201_1_a8/