Transition of type in the von Neumann algebras associated to the Connes-Marcolli $GS{p}_4$-system

We study different types of von Neumann algebras arising from the Connes-Marcolli $GS{p}_4$-system and show that a phase transition occurs at the level of these algebras. More precisely, we show that the type of these algebras transitions from type $I_{\mathrm{\infty }}$ to type $II{I}_1$, with this transition occurring precisely at the inverse temperature $\beta =4$.