Heis}^{(p)}$ in the XY and Heisenberg models, cf. table \[Tab1\]. The computational time for a particular fixed field $h$ is, therefore, significantly prolonged. Moreover, in order to screen the vicinity of the phase transition field $h_t^{(p)}$, multiple calculations for a sequence of magnetic fields $h$ had to be performed. As a consequence, in order to restrict the total computational time, we have analyzed the TFIM on the hyperbolic lattices up to $p=10$ only. (Notice that the number of block spins states kept was $m=20$ for $p \in \{4,5, \dots, 8\}$, and only $m=4$ for $p \in \{9,10\}$, which was sufficient due to exponentially weak correlations caused by the hyperbolic lattice geometry [@hctmrg-Ising-3-q]; any further increase of the states kept $m$ has not improved the numerical calculations significantly).

We have analyzed the phase transition of the TFIM by the expectation value of the spontaneous magnetization $\langle S_p^{z} \rangle$ as well as by the magnetic susceptibility $\chi_p$. Solving the minimization problem in , we received the optimal tensor elements $W^*_p(\{\sigma\})$, which uniquely define the approximative ground state $|\Psi_p^*\rangle$ via . Once $|\Psi_p^*\rangle$ has been constructed, we evaluated the spontaneous magnetization $$\langle S_p^{z} \rangle = \frac{\langle \Psi^*_p | S_{c}^{z} |\Psi^*_p \rangle}
                                    {\langle \Psi^*_p 