that TPVF applied to the models on the square lattice is less accurate than on the hyperbolic lattices ($p>4$).

The ground-state energies $E_0^{(p)}$ of the XY and the Heisenberg models have been studied in the absence of magnetic field on the series of the regular lattices with $4\leq p \leq 11$. Since no spontaneous symmetry breaking occurs in the two models at $h=0$, the spin-inversion symmetry helps to accelerate the TPVF algorithm due to significant reduction of the number of the free variational parameters. The resulting dependence of the ground-state energy per bond $E_0^{(p)}$ on the lattice geometry $p$ differs considerably for the two models. While the energies $E_0^{(p)}$ of the XY model form a monotonically increasing and exponentially saturated sequence with increasing $p$, the Heisenberg model induces a saw-like dependence containing the separated upper (odd $p$) and the lower (even $p$) branches, both of them converging exponentially fast to the common asymptotic value $E_0^{(\infty)}$ which corresponds to the ground-state energy on the Bethe lattice with the coordination number four.

We have analyzed the phase transition magnetic fields $h_t^{(p)}$ of the TFIM by the expectation value of the spontaneous magnetization $\langle S_p^z \rangle$, the associated magnetic exponent $\beta_p$, and the 