On factors associated with quantum Markov states corresponding to nearest neighbor models on a Cayley tree

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/73158In this paper we consider nearest neighbour models where the spin takes values in the set $Φ=\{\z_1,\z_2,...,\z_q\}$ and is assigned to the vertices of the Cayley tree ${\G}^k$. The Hamiltonian is defined by some given $λ$-function. We find a condition for the function $λ$ 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 $λ$-model. Also we give some physical applications of the obtained result.15 pagesOperator AlgebrasMathematical Physics47A67; 47L90; 47N55; 82B20On factors associated with quantum Markov states corresponding to nearest neighbor models on a Cayley treetext