GIBBS MEASURES FOR THE ASYMMETRIC CLOCK MODEL ON A CAYLEY TREE

Muzaffar Rahmatullaev; Bunyod Abraev

GIBBS MEASURES FOR THE ASYMMETRIC CLOCK MODEL ON A CAYLEY TREE

Abstract

We consider the $p$-state clock model on the Cayley tree and derive a system of functional equations governing this model. Each positive solution of the system corresponds to a splitting Gibbs measure. Utilizing this framework, we investigate the translation-invariant splitting Gibbs measures (TISGMs) of the four-state clock model on the Cayley tree of order two.

Keywords

Thanks

The authors express their sincere gratitude to Professor U. A. Rozikov for his careful review of this paper and for providing valuable insights and constructive feedback. The authors also thank the referees for the careful reading of the manuscript and especially for a number of suggestions that have improved the paper.

References

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Details

Primary Language

English

Subjects

Algebra and Number Theory

Journal Section

Research Article

Authors

Muzaffar Rahmatullaev This is me
0000-0003-2987-7714
Uzbekistan

Bunyod Abraev ^* This is me
0000-0003-1645-6662
Uzbekistan

Publication Date

June 9, 2026

Submission Date

April 25, 2025

Acceptance Date

August 12, 2025

Published in Issue

Year 2026 Volume: 16 Number: 6

IZ

https://izlik.org/JA57DB24SK

Cite

RIS / Bibtex

APA

Rahmatullaev, M., & Abraev, B. (2026). GIBBS MEASURES FOR THE ASYMMETRIC CLOCK MODEL ON A CAYLEY TREE. TWMS Journal of Applied and Engineering Mathematics, 16(6), 713-724. https://izlik.org/JA57DB24SK

AMA

1.Rahmatullaev M, Abraev B. GIBBS MEASURES FOR THE ASYMMETRIC CLOCK MODEL ON A CAYLEY TREE. JAEM. 2026;16(6):713-724. https://izlik.org/JA57DB24SK

Chicago

Rahmatullaev, Muzaffar, and Bunyod Abraev. 2026. “GIBBS MEASURES FOR THE ASYMMETRIC CLOCK MODEL ON A CAYLEY TREE”. TWMS Journal of Applied and Engineering Mathematics 16 (6): 713-24. https://izlik.org/JA57DB24SK.

EndNote

Rahmatullaev M, Abraev B (June 1, 2026) GIBBS MEASURES FOR THE ASYMMETRIC CLOCK MODEL ON A CAYLEY TREE. TWMS Journal of Applied and Engineering Mathematics 16 6 713–724.

IEEE

[1]M. Rahmatullaev and B. Abraev, “GIBBS MEASURES FOR THE ASYMMETRIC CLOCK MODEL ON A CAYLEY TREE”, JAEM, vol. 16, no. 6, pp. 713–724, June 2026, [Online]. Available: https://izlik.org/JA57DB24SK

ISNAD

Rahmatullaev, Muzaffar - Abraev, Bunyod. “GIBBS MEASURES FOR THE ASYMMETRIC CLOCK MODEL ON A CAYLEY TREE”. TWMS Journal of Applied and Engineering Mathematics 16/6 (June 1, 2026): 713-724. https://izlik.org/JA57DB24SK.

JAMA

1.Rahmatullaev M, Abraev B. GIBBS MEASURES FOR THE ASYMMETRIC CLOCK MODEL ON A CAYLEY TREE. JAEM. 2026;16:713–724.

MLA

Rahmatullaev, Muzaffar, and Bunyod Abraev. “GIBBS MEASURES FOR THE ASYMMETRIC CLOCK MODEL ON A CAYLEY TREE”. TWMS Journal of Applied and Engineering Mathematics, vol. 16, no. 6, June 2026, pp. 713-24, https://izlik.org/JA57DB24SK.

Vancouver

1.Muzaffar Rahmatullaev, Bunyod Abraev. GIBBS MEASURES FOR THE ASYMMETRIC CLOCK MODEL ON A CAYLEY TREE. JAEM [Internet]. 2026 Jun. 1;16(6):713-24. Available from: https://izlik.org/JA57DB24SK