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Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

Abstract

In this paper it is found fixed points of Lyapunov integral equation and considered the connections between Gibbs measures for four competing interactions of models with uncountable (i.e. $[0,1]$) set of spin values on the Cayley tree of order two.

First Page

19

Last Page

23

References

1. Eshkabilov Yu. Kh, Haydarov F. H., Rozikov U. A. Uniqueness of Gibbs measure for models with uncountable set of spin values on a Cayley tree. Math. Phys. Anal. Geom., 2013, V.16, pp.1–17.

2. Georgii H. O. Gibbs Measures and Phase Transitions, 2nd edn. De Gruyter Studies in Mathematics, Vol. 9. Walter de Gruyter, Berlin, 2011. – 545 p.

3. Krasnosel’ski M. A. Positive Solutions of Opertor Equations. Fizmatgiz, Moscow, 1962 (Russian). – 394 p.

4. Nirenberg L. Topics in nonlinear functional analysis. AMS, Courant Lec. Notes in Math, 6, N.Y., 2001. – 145 p.

5. Rozikov U. A., Haydarov F. H. Four competing interactions for models with an uncountable set of spin values on a Cayley tree. Theor. Math. Phys., 2017, V. 191, No. 3, pp.910–923.

6. Rozikov U. A. Gibbs measures on Cayley trees. World Scientific, 2013. – 404 p.

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