Gibbs measures for the Potts model with a countable set of spin values on a Cayley tree

We consider an infinite system of functional equations for the Potts model with competing interactions of radius $$r=2$$ and countable spin values $$\Phi=\{0,1,\ldots,\}$$ on the Cayley tree of order $$k=2$$ . We reduce the problem to the description of the solutions of some infinite system of equations for any $$k=2$$ and any fixed probability measure $$\nu$$ with $$\nu(i)>0$$ on the set of all nonnegative integer numbers. We also give a description of the class of measures $$\nu$$ on $$\Phi$$ such that the infinite system of equations has unique solution $$\{a^i,\,i=1,2,\ldots\}$$ , $$a\in(0,1)$$ , with respect to each element of this class.

Ҳали таржима қилинмаган