($s=1$) and partially disordered ($s\neq 1$) systems. When $m \to \infty$ (infinite discretization), for completely ordered systems ($s=1$), we observed an infinite increase in value of $n_c$ in the longitudinal direction, whereas such increase was finite in the transversal direction (see dashed lines in Fig. \[fig:II\_pc\_vs\_nc\]). For partially disordered ($s\neq 1$) systems, such increase was always finite in both directions.

![Critical number density, $n_c$, versus the critical filling ratio, $p_c$ at different values of $m$ and the order parameter, $s$. Here, the filled and open symbols correspond to the longitudinal and transversal directions, respectively. The lines are provided simply as visual guides. \[fig:II\_pc\_vs\_nc\]](ncvspc "fig:"){width="0.9\linewidth"}\

The data obtained from the $p_c(m)$ dependencies were used for fitting with the power equation $1/n_c(m)=1/n_c(\infty)+\alpha/m^\beta$ and for evaluation of the values of $n_c(\infty)$. The examples of such fittings are presented in Fig. \[fig:C04\_fitting\].

![Examples of fittings of $1/n_c$ versus $1/m$ with the power equation $1/n_c(m)=1/n_c(\infty)+\alpha/m^\beta$ used for evaluation of the values of $n_c(\infty)$. Here, $\alpha$ and $\beta$ are the fitting parameters. \[fig:C04\_fitting\]](ncvsmrep "fig:"){width="0.9\linewidth"}\

Figure \[C05\_nr\_vs\_s\] presents the relative critical number density, $n^*=n_c/n_c^i$, versus the order parameter, $s$. Here, the values were obtained in the limit of $m\rightarrow\infty$ and where $n_c^i$ corresponds to the isotropic case, 