  In this paper we consider nearest neighbour models where the spin takes
values in the set $\Phi=\{\z_1,\z_2,...,\z_q\}$ and is assigned to the vertices
of the Cayley tree ${\G}^k$. The Hamiltonian is defined by some given
$\lambda$-function. We find a condition for the function $\lambda$ to determine
the type of the von Neumann algebra generated by the GNS - construction
associated with the quantum Markov state corresponding to the unordered phase
of the $\lambda$-model. Also we give some physical applications of the obtained
result.
