ansatz for the ground-state in the form of the Tensor product state (TPS) [@Orus] with the Corner transfer matrix renormalization group (CTMRG) scheme [@Nishino]. This algorithm can be used to study quantum spin systems in the thermodynamic limit on regular hyperbolic lattices of constant negative Gaussian curvature [@Sadoc]. The hyperbolic lattices are constructed by tessellation of congruent $p$-sided polygons (with the coordination number fixed to four). We applied the modified TPVF algorithm to the Euclidean square ($p = 4$) and hyperbolic pentagonal ($p = 5$) lattices in order to analyze the critical phenomena of the XY, Heisenberg and transverse field Ising model (TFIM). On the square lattice numerical inaccuracy varied from $1.2\%$ in the XY model to $3.7\%$ in TFIM at the phase transition. This observation originates in the mean-field-like behavior induced by the TPS ansatz, which, as a consequence, cannot accurately approximate the correct ground state of the TFIM on the two-dimensional Euclidean lattice, which belongs to the Ising universality class. On the contrary, since the Hausdorff dimension of the hyperbolic lattices is infinite, spin models on these lattices belong to the mean-field universality class due to short range correlations, even though the mean-field approximation of the Hamiltonian is 