5 random lattice. For values q < q$_{c}$ ≈ 0 . 35, a second-order transition takes place since in the lim$_{N}$ →∞ (2 / 3 − B$_{i,min}$ ) = 0, even at T$_{c}$ . However, for q > q$_{c}$ a first-order transition is observed, because one has (2 / 3 − B$_{i,min}$ ) = 0. For instance, for q = 0 . 4 we get (2 / 3 − B$_{min}$ ) = 0 . 273(3). In Fig. 9 the fourth-order Binder cumulant is shown as a function of the K for several values of N and q = 0 . 1. Taking the largest lattices we have K$_{c}$ = 0 . 3109(6). To estimate U ∗ 4 we note that it varies little at K$_{c}$ so we have U ∗ 4 = 0 . 326(4). From the second-order cumu- lant (not shown) we similarly get K$_{c}$ = 0 . 31078(3) and U ∗ 2 = 0 . 538(2). For other values of q we have: for q = 0 . 2, K$_{c}$ = 0 . 3114(6) and U ∗ 4 = 0 . 326(5) and K$_{c}$ = 0 . 31164(5) and U ∗ 2 = 0 . 534(7); for q = 0 . 3, K$_{c}$ = 0 . 32154(8) and U ∗ 4 = 0 . 327(5), and K$_{c}$ = 0 . 32137(5) and U ∗ 2 = 0 . 556(4). One can see that the agreement of the critical temper- ature is quite good and U ∗ 4 is definitely different from the universal value U ∗ 4 ∼ 0 . 61 for the same model on the regular 2 D lattice and undirected Voronoi-Delaunay In our analysis we also computed the modulus of the magnetization at the inflection point, T = T$_{c}$ for q = 0 . 1 , 0 . 2 , and 0 . 3 . The logarithm of these quantities as a function of the logarithm of L are presented in Figure 11. A linear fit of these data gives β/ν = 0 . 421(7) , 0 . 400(5) and 0 . 338(5) from the magnetization for q = 0 . 1 , 0 . 2, and 0 . 3, respectively. These results are totally different of β/ν = 0 . 125 obtained for a regular 2 D lattice. FIG. 7: The same display the Fig. 6, but now for q = 0 . 4 and size N = 250 , 500 , 1000 , 2000 , 4000 , 8000, and 16000 from bottom to top. FIG. 9: Fourth-order Binder cumulant as a function of K for several values of the system size N = 500 , 1000 , 2000 , 4000 , 8000 and 16000, and q = 0 . 1. FIG. 8: Plot of 2 / 3 − B$_{min}$ at T$_{c}$ as a function of log- arithm of 1 /N for several values of the system size N = 250 , 500 , 1000 , 2000 , 4000 , 8000 and 16000, and q = 0 . 1 , 0 . 2, 0 . 3, and 0 . 4. In Fig. 12 the logarithm plot of the susceptibility at T$_{c}$ as a function of the logarithm of L = N 1 / 2 is pre- sented. A linear fit of these data gives, at T = T$_{c}$ , γ/ν = 1 . 101(4) , 1 . 138(5) and 1 . 312(7). Similarly, from the maximum of the magnetic susceptibility (not shown) one gets γ/ν = 1 . 130(14) , 1 . 156(12) and 1 . 312(3) for 0.320 0.328 0.336 0.344 K 0.10 0.20 0.30 0.40 0.50 0.60 0.70 B(K) 250 q=0.4 16000 0.308 0.310 0.312 0.314 K 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 U 4 16000 500 q=0.1 0 0.001 0.002 0.003 0.004 1/N 0 0.1 0.2 0.3 0.4 0.5 2/3-B min (k) q=0.1 q=0.2 q=0.3 q=0.4 0.366 0.368 0.370 0.372 0.374 0.376 0.378 0.380 K -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 U 4 q=0.9 250 1000 500 2000 4000 16000 8000 Fig. 10 displays the behavior of the magnetization fourth-order cumulant for q = 0 . 9 in a narrow range of K , where one can note a different behavior leading to a first-order phase transition. FIG. 10: Fourth-order Binder cumulant as a func- tion of K for several values of the system size N = 250 , 500 , 1000 , 2000 , 4000 , 8000 and 16000, and q = 0 . 9.