$h_t^{(p)}$ of the TFIM including the estimated errors $\Delta^{(p)}$ with respect to the lattice parameter $p$.

\[Tab3\]

Another independent way of obtaining (and confirming) the phase transition fields $h_t^{(p)}$ can be carried out by analyzing the magnetic susceptibility $$\chi_p=-\frac{\partial^2 E_0^{(p)}}{\partial h^2}\, .
\label{chi}$$ The functional dependence of the susceptibility on the magnetic field $h$ is shown in figure \[Fig6\]. A non-diverging discontinuity of $\chi_p$ occurs at the identical phase transition fields $h_t^{(p)}$, which we have determined above by the spontaneous magnetization analysis and are depicted by the vertical dot-dashed lines. The inaccuracy comes from performing the second derivative in  numerically, and the additional improvement rests in decreasing the spacing interval $\delta h$, i.e, in shrinking the distance between the magnetic fields, at which the ground-state energy is evaluated by TPVF. In the limit $\delta h \to 0$, the magnetic susceptibility undergoes a discontinuous jump at $h_t^{(p)}$ [@DaniskaGendiar]. It is obvious that there is no significant difference between the phase transition magnetic fields $h_t^{(p)}$ obtained by the analysis of the transverse magnetization $\langle S_p^{z}\rangle$ and the magnetic susceptibility $\chi_p$.

Except for the analysis of the phase transition by the spontaneous magnetization $\langle S_p^{z}\rangle$ and the magnetic susceptibility $\chi_p$, the field dependence 