Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 2 of 2
Full-Text Articles in Physical Sciences and Mathematics
Translation-Invariant Gibbs Measures Of A Model On Cayley Tree, Golibjon Botirov
Translation-Invariant Gibbs Measures Of A Model On Cayley Tree, Golibjon Botirov
Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences
We consider a model where the spin takes values in the set [0,1]d, and is assigned to the vertexes of the Cayley tree. We reduce the problem of describing the “splitting Gibbs measures” of the model to the description of the solutions of some non-linear integral equation. For a concrete form of the Kernel of the integral equation we show the uniqueness of solution.
Positive Fixed Points Of Lyapunov Integral Operators And Gibbs Measures, Farkhod Haydarov
Positive Fixed Points Of Lyapunov Integral Operators And Gibbs Measures, Farkhod Haydarov
Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences
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.