F. M. Mukhamedov, Ch. Pah, H. Jamil, “Ground states and phase transition of the $\lambda$ model on the Cayley tree”, TMF, 194:2 (2018), 304–319; Theoret. and Math. Phys., 194:2 (2018), 260

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Teoreticheskaya i Matematicheskaya Fizika, 2018, Volume 194, Number 2, Pages 304–319
DOI: https://doi.org/10.4213/tmf9309 (Mi tmf9309)

This article is cited in 8 scientific papers (total in 8 papers)

Ground states and phase transition of the

$\lambda$ model on the Cayley tree

F. M. Mukhamedov^a, Ch. Pah^b, H. Jamil^b

^a Department of Mathematical Sciences, College of Science, United Arab Emirates University, Al Ain, UAE
^b Department of Computational and Theoretical Sciences, Faculty of Science, International Islamic University Malaysia, Kuantan, Malasia

Full-text PDF (544 kB) Citations (8)

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DOI: https://doi.org/10.4213/tmf9309

Abstract: We consider the

$\lambda$ model, a generalization of the Potts model, with spin values

$\{1,2,3\}$ on the order-two Cayley tree. We describe the model ground states and prove that translation-invariant Gibb measures exist, which means that a phase transition exists. We establish that two-periodic Gibbs measures exist.

Keywords: ground state, phase transition, Gibbs measure.

Received: 28.11.2016

English version:
Theoretical and Mathematical Physics, 2018, Volume 194, Issue 2, Pages 260–273
DOI: https://doi.org/10.1134/S004057791802006X

Bibliographic databases:

Language: Russian

Citation: F. M. Mukhamedov, Ch. Pah, H. Jamil, “Ground states and phase transition of the

$\lambda$ model on the Cayley tree”, TMF, 194:2 (2018), 304–319; Theoret. and Math. Phys., 194:2 (2018), 260–273

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Linking options:

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https://doi.org/10.4213/tmf9309

https://www.mathnet.ru/eng/tmf/v194/i2/p304

This publication is cited in the following 8 articles:

M. T. Makhammadaliev, “Pure phases of the ferromagnetic Potts model with $q$ states on the Cayley tree of order three”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 34:4 (2024), 499–517
M. M. Rahmatullaev, B. M. Isakov, “Ground states of Ising-Potts model on Cayley tree”, Ufa Math. J., 15:1 (2023), 43–55
F. Mukhamedov, “Extremality of disordered phase of $\lambda$ -model on Cayley trees”, Algorithms, 15:1 (2022), 18
F. M. Mukhamedov, M. M. Rahmatullaev, M. A. Rasulova, “Extremality of translation-invariant Gibbs measures for the $\lambda$ -model on the binary Cayley tree”, Theoret. and Math. Phys., 210:3 (2022), 411–424
F. Mukhamedov, Ch. H. Pah, H. Jamil, M. Rahmatullaev, “On ground states and phase transition for lambda-model with the competing Potts interactions on Cayley trees”, Physica A, 549 (2020), 124184
Farrukh M. Mukhamedov, Muzaffar M. Rahmatullaev, M. A. Rasulova, “Slabo periodicheskie osnovnye sostoyaniya dlya λ-modeli”, Ukr. Mat. Zhurn., 72:5 (2020)
F. M. Mukhamedov, M. M. Rakhmatullaev, M. A. Rasulova, “Weakly periodic ground states for the lambda-model”, Ukr. Math. J., 72:5 (2020), 771–784
Mukhamedov F. Pah Ch.H. Jamil H., “Lambda-Model With Competing Potts Interactions on Cayley Tree of Order 2”, AIP Conference Proceedings, 2013, ed. Zin S. Abdullah N. Khazali K. Roslan N. Rusdi N. Saad R. Yazid N. Zain N., Amer Inst Physics, 2018, 020032

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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Abstract page:	476
Full-text PDF :	129
References:	64
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