Free energy and entropy for the constructive Gibbs measures of the Ising model on the Cayley tree of order three
https://doi.org/10.17586/2220-8054-2025-16-3-261-273
Abstract
In this paper, we identify non-translation-invariant constructive Gibbs measures for the Ising model on a third-order Cayley tree, which differ from known ones. We provide the conditions for the existence of at least two distinct Gibbs measures, which implies that a phase transition occurs. The free energies and entropies corresponding to the identified measures are calculated. These free energies and entropies are then compared with the known ones and shown to differ from them.
Supporting agencies: The authors thank Obid Sh. Karshiboev for valuable advice and an anonymous referee for helpful suggestions that improved the paper.
About the Authors
M. M. Rahmatullaev
V. I. Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences; New Uzbekistan University
Uzbekistan
Uzbekistan
Muzaffar M. Rahmatullaev
4-b, University str, 100174, Tashkent
100000, Tashkent
Z. A. Burxonova
Namangan State University; Namangan State Technical University
Russian Federation
Russian Federation
Zulxumor A. Burxonova
161, Boburshox str, 160107, Namangan
12, Islom Karimov str, 160103, Namangan
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Review
For citations:
Rahmatullaev M.M., Burxonova Z.A. Free energy and entropy for the constructive Gibbs measures of the Ising model on the Cayley tree of order three. Nanosystems: Physics, Chemistry, Mathematics. 2025;16(3):261-273. https://doi.org/10.17586/2220-8054-2025-16-3-261-273
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