Abstract
In the present paper, we consider a quantum Markov chain corresponding to the XY-model with competing Ising interactions on the Cayley tree of order two. Earlier, it was proved that this state does exist and is unique. Moreover, it has clustering property. This means that the von Neumann algebra generated by this state is a factor. In the present paper, we establish that the factor generated by this state may have type \(\mathop {\mathrm{III_{\lambda }}}\)\(\lambda \in (0,1)\) which is unusual for states associated with models with nontrivial interactions.
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