  In the present paper, the Ising model with mixed spin-(1,1/2) is considered
on the second order Cayley tree. A construction of splitting Gibbs measures
corresponding the model is given which allows to establish the existence of the
phase transition (non-uniqueness of Gibbs measures). We point out that, in the
phase transition region, the considered model has three translation-invariant
Gibbs measures in the ferromagnetic and anti-ferromagnetic regimes, while the
classical Ising model does not possesses such Gibbs measures in the
anti-ferromagnetic regime. It turns out that the considered model, like the
Ising model, exhibits a disordered Gibbs measure. Therefore, non-extremity and
extremity of such disordered Gibbs measures is investigated by means of
tree-indexed Markov chains.
