are of order $O(\sqrt{N})$ for $N_c$ and $L_c$, and $O(1/\sqrt{N})$ for $\alpha_{eff}$. So to obtain a large $N$ limit, we define $\chi_c(\alpha) \equiv {\mbox{Var}}(N_c)/N$, $\chi_l(\alpha) \equiv
{\mbox{Var}}(L_c)/N$ and $\chi_\alpha(\alpha) \equiv N\ {\mbox{Var}}(2L_c/N_c)$. These quantities are analogous in the spin models to the magnetic susceptibility (equivalent to the fluctuations of the magnetization).

![*Monte-Carlo estimations of $\chi_\alpha(\alpha)$ (variance of the average connectivity of the core) versus $(\alpha-e)$. The axes are labeled by decimal logarithms.*[]{data-label="fig:av"}](av.eps){width="\figwidth"}

On Fig. \[fig:var\], Monte-Carlo estimations of $\chi_c$ and $\chi_l$ show that $\chi_c(\alpha)$ and $\chi_l(\alpha)$ have a finite limit for $N=\infty$ when $\alpha>e$, a vanishing limit when $\alpha < e$ and diverge when $\alpha$ approaches the critical value $e$. By analogy with $c(\alpha) \sim
l(\alpha) \sim (\alpha-e)$ and $\alpha_{eff}-2 \sim (\alpha -e)^{1/2}$ when $\alpha\to e^{+}$, power laws are expected for the divergences. So, we define two critical exponents $\rho$ and $\rho'$ by $$\begin{aligned}
  \chi_c(\alpha) \sim \chi_l(\alpha) & \sim & (\alpha-e)^{-\rho}, 
        \label{eq:rho} \\
  \chi_\alpha(\alpha)                & \sim & (\alpha-e)^{-\rho'},
        \label{eq:rho2}\end{aligned}$$ when $\alpha\to e^{+}$. The exponent $\rho$ could be numerically measured by plotting $\log(\chi_c)$ or $\log(\chi_l)$ versus $\log(\alpha-e)$. Unfortunately, this gives poor results because the curvature of the plot is too important, with a slope $\rho$ changing from 1 to 0.5. But 