|                   \Psi^*_p \rangle} \, ,
\label{sz}$$ where ${c}$ labels an arbitrary spin in the central polygon of the lattice in order to suppress boundary effects. The resulting dependence of the magnetization $\langle S_p^{z}\rangle$ with respect to the magnetic field $h$ near the phase transition field $h_t^{(p)}$ is plotted in the upper graph of figure \[Fig4\]. The quantum phase transition of the TFIM is characterized by a non-analytic behavior of the magnetization curve, when $\langle S_p^{z}\rangle \to 0$ if approaching the phase transition field $h \to h_t^{(p)}$ from the ordered phase ($h < h_t^{(p)}$). The phase transition exponent $\beta_p$, which depends on the lattice geometry, describes the singularity through the scaling relation in the ordered phase $$\langle S_p^z (h) \rangle \propto {\left(h_t^{(p)} - h \right)}^{\beta_p} \, .
\label{powerlaw}$$ Figure \[Fig4\] (the lower graph) shows the squared transversal magnetization $ {\langle S_p^{z}\rangle}^{2}$, where we point out the linearity of the squared magnetization if approaching the phase transition field $h_t^{(p)}$. Such a dependence confirms the mean-field exponent $\beta_p=\frac{1}{2}$ regardless of the lattice parameter $p$, which results in the mean-field-like behavior of the TFIM if approaching the phase transition.

![The spontaneous magnetization $\langle S_p^{z}\rangle$ (the upper graph) and its square ${\langle S_p^{z}\rangle}^{2}$ (the lower 