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Teoreticheskaya i Matematicheskaya Fizika, 2020, Volume 205, Number 1, Pages 146–155
DOI: https://doi.org/10.4213/tmf9893 (Mi tmf9893) 		 
Phase transitions for models with a continuum set of spin values on a Bethe lattice

Yu. Kh. Eshkabilova, G. I. Botirovb, F. H. Haydarovc

a Karshi State University, Kashkhadaryo, Uzbekistan
b Institute of Mathematics, Tashkent, Uzbekistan
c National University of Uzbekistan, Tashkent, Uzbekistan
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DOI: https://doi.org/10.4213/tmf9893
Abstract: We consider a model with nearest-neighbor interactions and the set $[0,1]$ of spin values on a Bethe lattice {(}Cayley tree{\rm)} of arbitrary order. This model depends on a continuous parameter $\theta$ and is a generalization of known models. For all values of $\theta$, we give a complete description of the set of translation-invariant Gibbs measures of this model.
Keywords: Cayley tree, spin value, Gibbs measure, Hammerstein's equation, fixed point.
Received: 23.02.2020
Revised: 10.04.2020
English version:
Theoretical and Mathematical Physics, 2020, Volume 205, Issue 1, Pages 1372–1380
DOI: https://doi.org/10.1134/S0040577920100104
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: Yu. Kh. Eshkabilov, G. I. Botirov, F. H. Haydarov, “Phase transitions for models with a continuum set of spin values on a Bethe lattice”, TMF, 205:1 (2020), 146–155; Theoret. and Math. Phys., 205:1 (2020), 1372–1380
Citation in format AMSBIB
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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