Translation-invariant Gibbs measures for the mixed spin-1/2 and spin-1 Ising model with an external field on a Cayley tree
https://doi.org/10.17586/2220-8054-2024-15-5-576-585
Abstract
Phase transitions of the mixed spin-1/2 and spin-1 Ising model under the presence of an external field on the general order Cayley tree are investigated within the framework of the tree-indexed Markov chains. We find the conditions that ensure the existence of at least three translation-invariant Gibbs measures for the model on the Cayley tree of order k. We are able to solve the model exactly on the binary tree (k = 2) under the specific external field. The main attention is paid to the systematic study of the structure of the set of the Gibbs measures. We find the extremality and non-extremality regions of the disordered phase of the model on the binary tree.
Supporting agencies: We thank Professor F. M. Mukhamedov for his participation in discussions of the results. We also thank the anonymous referee for reading the manuscript carefully and for making valuable suggestions.
About the Authors
Muzaffar M. Rahmatullaev
V. I. Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences; New Uzbekistan University; Namangan state University
Uzbekistan
Uzbekistan
Muzaffar M. Rahmatullaev – V. I. Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences,
4-b, University str, 100174; 100000, Tashkent; 316, Uychi str, Namangan
Dilshod O. Egamov
V. I. Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences; Namangan state University
Uzbekistan
Uzbekistan
Dilshod O. Egamov – V. I. Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences
4-b, University str,100174, Tashkent; 316, Uychi str, Namangan
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Review
For citations:
Rahmatullaev M.M., Egamov D.O. Translation-invariant Gibbs measures for the mixed spin-1/2 and spin-1 Ising model with an external field on a Cayley tree. Nanosystems: Physics, Chemistry, Mathematics. 2024;15(5):576-585. https://doi.org/10.17586/2220-8054-2024-15-5-576-585
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