1202.1722 (Yu. Kh. Eshkabilov et al.)

Uniqueness of Gibbs Measure for Models With Uncountable Set of Spin
Values on a Cayley Tree    [PDF]

Yu. Kh. Eshkabilov, F. H. Haydarov, U. A. Rozikov

We consider models with nearest-neighbor interactions and with the set
$[0,1]$ of spin values, on a Cayley tree of order $k\geq 1$.
It is known that the "splitting Gibbs measures" of the model can be described
by solutions of a nonlinear integral equation. For arbitrary $k\geq 2$ we find
a sufficient condition under which the integral equation has unique solution,
hence under the condition the corresponding model has unique splitting Gibbs
measure.

View original: http://arxiv.org/abs/1202.1722