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TMF, 2020, Volume 205, Number 1, Pages 146–155 (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

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.
Author to whom correspondence should be addressed

DOI: https://doi.org/10.4213/tmf9893

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English version:
Theoretical and Mathematical Physics, 2020, 205:1, 1372–1380

Bibliographic databases:

Received: 23.02.2020
Revised: 10.04.2020

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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\by Yu.~Kh.~Eshkabilov, G.~I.~Botirov, F.~H.~Haydarov
\paper Phase transitions for models with a~continuum set of spin values on
a~Bethe~lattice
\jour TMF
\yr 2020
\vol 205
\issue 1
\pages 146--155
\mathnet{http://mi.mathnet.ru/tmf9893}
\crossref{https://doi.org/10.4213/tmf9893}
\transl
\jour Theoret. and Math. Phys.
\yr 2020
\vol 205
\issue 1
\pages 1372--1380
\crossref{https://doi.org/10.1134/S0040577920100104}
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  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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