Author： Rozikov Utkir
Publisher： Springer Publishing Company
ISSN： 1385-0172
Source： Mathematical Physics, Analysis and Geometry, Vol.13, Iss.3, 2010-09, pp. : 275-286
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Abstract
We consider models with nearest-neighbor interactions and with the set [0, 1] of spin values, on a Cayley tree of order k 1. We reduce the problem of describing the “splitting Gibbs measures” of the model to the description of the solutions of some nonlinear integral equation. For k = 1 we show that the integral equation has a unique solution. In case k 2 some models (with the set [0, 1] of spin values) which have a unique splitting Gibbs measure are constructed. Also for the Potts model with uncountable set of spin values it is proven that there is unique splitting Gibbs measure.
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