NEW WEAKLY PERIODIC  ADIC GENERALIZED GIBBS MEASURE FOR THE  ADIC ISING MODEL ON THE CAYLEY TREE OF ORDER TWO: NEW WEAKLY PERIODIC  ADIC GENERALIZED GIBBS MEASURE FOR THE  ADIC ISING MODEL ON THE CAYLEY TREE OF ORDER TWO

Muzaffar Raxmatullayev; Zulxumor Abdukaxorova

doi:10.52754/16948645_2023_2_195

NEW WEAKLY PERIODIC ADIC GENERALIZED GIBBS MEASURE FOR THE ADIC ISING MODEL ON THE CAYLEY TREE OF ORDER TWO

Authors

Muxammadjanovich Institute of Mathematics named after V.I. Romanovsky of the Academy of Sciences of the Republic of Uzbekistan
Tuxtasinovna Namangan State University

DOI:

https://doi.org/10.52754/16948645_2023_2_195

Keywords:

Cayley tree, adic numbers, adic Ising model, Gibbs measure, weakly periodic Gibbs measure.

Abstract

In the present paper, we study the adic Ising model on the Cayley tree of order two. The existence of -weakly periodic (non-periodic) adic generalized Gibbs measures for this model is proved.

References

V. S. Vladimirov, I. V. Volovich and E. V. Zelenov, p -Adic Analysis and Mathematical Physics (World Sci. Publ., Singapore,1994). DOI: https://doi.org/10.1142/1581

U. A. Rozikov, Gibbs Measures on Cayley Trees (World Sci. Publ., Singapore, 2013). DOI: https://doi.org/10.1142/8841

Rozikov U. A., Rahmatullaev M. M. Description of weakly periodic Gibbs measures for the Ising model on a Cayley tree. Theor. Math.Phys., 156(2): (2008). DOI: https://doi.org/10.1007/s11232-008-0091-y

Khakimov O. N. On a Generalized p-adic Gibbs Measure for Ising Model on Trees. p-Adic Numbers, Ultrametric Anal. Appl., 6(3), 2014, pp.207-217. DOI: https://doi.org/10.1134/S2070046614030042

Rahmatullaev M. M. "On new weakly periodic Gibbs measures of the Ising model on the Cayley tree of order 6". J. Phys.: Conf. Ser., 697 (2016), 012020, pp.7. DOI: https://doi.org/10.1088/1742-6596/697/1/012020

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Published

2023-12-30

How to Cite

Raxmatullayev, M., & Abdukaxorova, Z. (2023). NEW WEAKLY PERIODIC ADIC GENERALIZED GIBBS MEASURE FOR THE ADIC ISING MODEL ON THE CAYLEY TREE OF ORDER TWO: NEW WEAKLY PERIODIC ADIC GENERALIZED GIBBS MEASURE FOR THE ADIC ISING MODEL ON THE CAYLEY TREE OF ORDER TWO. Journal of Osh State University. Mathematics. Physics. Technical Sciences, (2(3), 195–202. https://doi.org/10.52754/16948645_2023_2_195

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Issue

No. 2(3) (2023): Journal of Osh State University. Mathematics. Physics. Technical Sciences

Section

MATHEMATICS

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This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

NEW WEAKLY PERIODIC ADIC GENERALIZED GIBBS MEASURE FOR THE ADIC ISING MODEL ON THE CAYLEY TREE OF ORDER TWO