Uniqueness of Gibbs Measure for Models With Uncountable Set of Spin   Values on a Cayley Tree
  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. 
Yu. Kh. Eshkabilov, F. H. Haydarov, U. A. Rozikov
math.FA math-ph math.MP