SOME CONSTRUCTIVE  -ADIC GENERALIZED GIBBS MEASURES FOR THE ISING MODEL ON A CAYLEY TREE: SOME CONSTRUCTIVE  -ADIC GENERALIZED GIBBS MEASURES FOR THE ISING MODEL ON A CAYLEY TREE

Muzaffar Rahmatullaev; Akbarkhuja Tukhtabaev

doi:10.52754/16948645_2023_2_187

Authors

Muhammadjanovich Namangan regional department, Institute of Mathematics named after V.I.Romanovsky
Mamajonovich Tukhtabaev Akbarkhuja Mamajonovich, PhD. student, Namangan state university

DOI:

https://doi.org/10.52754/16948645_2023_2_187

Keywords:

p-adic numbers, p-adic Ising model, Cayley tree, Gibbs measure, phase transition

Abstract

The paper is devoted to some non-periodic -adic generalized Gibbs measures for Ising model on a semi-Cayley tree of order . We construct uncountable non-periodic -adic generalized Gibbs measures for the Ising model on a semi-Cayley tree. We study the boundedness of the measures. Furthermore, we find conditions that guarantee existence of the phase transition.

References

U.A.Rozikov, Gibbs Measures on Cayley Trees, World Scientific Publisher, Singapore, 2013. DOI: https://doi.org/10.1142/8841

V.S.Vladimirov, I.V.Volovich and E.V.Zelenov, -Adic Analysis and Mathematical Physics, World Scientific Publisher, Singapore, 1994. DOI: https://doi.org/10.1142/1581

N.N.Ganikhodjayev, F.M.Mukhamedov, U.A.Rozikov, Existence of phase transition for the Potts -adic model on the set . Theor. Math. Phys. 130(2002), No.3, 425-431. DOI: https://doi.org/10.1023/A:1014723108030

O.N.Khakimov, On a generalized -adic Gibbs measure for Ising model on trees, -Adic Numbers Ultrametric Anal. Appl., 6(3), 207-217, 2014. DOI: https://doi.org/10.1134/S2070046614030042

F.M.Mukhamedov, On -adic quasi Gibbs measures for -state Potts model on the Cayley tree, -Adic Numbers, Ultrametric Anal. Appl., (2010), 241-251. DOI: https://doi.org/10.1134/S2070046610030064

H.Akin, U.A.Rozikov, S.Temir, A new set of limiting Gibbs measures for the Ising model on a Cayley tree, J.Stat. Phys., 142, 314-321, 2011. DOI: https://doi.org/10.1007/s10955-010-0106-6

M.M.Rahmatullaev and A.M.Tukhtabaev, Non periodic -adic generalized Gibbs measure for the Ising model, -Adic Numbers Ultrametric Anal. Appl., 11, 319-327, 2019. DOI: https://doi.org/10.1134/S207004661904006X

P.M.Bleher and N.N.Ganikhodjaev, On pure phases of the Ising model on the Bethe lattice, Theor. Probab. Appl., 35, 216-227, 1990. DOI: https://doi.org/10.1137/1135031

SOME CONSTRUCTIVE -ADIC GENERALIZED GIBBS MEASURES FOR THE ISING MODEL ON A CAYLEY TREE