3  1  10  100  1.56  1.58  1.6  1.62  1.64  1.66  1.68 8 16 32 64 128 k B T/J χ L = (3 , 4 , 6 , 4)  1  10  100  2.06  2.08  2.1  2.12  2.14  2.16  2.18  2.2 8 16 32 64 128 P Sfrag re placeme n ts k B T/J χ L = (3 , 4 , 6 , 4) (3 $^{4}$, 6)  0  0.1  0.2  0.3  0.4  0.5  0.6  0.7  0.8  0.9  1  1.3  1.4  1.5  1.6  1.7  1.8  1.9  2 8 16 32 64 128 M k B T/J L = (3 , 4 , 6 , 4)  0  0.1  0.2  0.3  0.4  0.5  0.6  0.7  0.8  0.9  1.8  1.9  2  2.1  2.2  2.3  2.4  2.5  2.6 8 16 32 64 128 PSf rag rep lac eme n ts M k B T/J L = (3 , 4 , 6 , 4) (3 $^{4}$, 6) FIG. 2: The magnetisation M as a function of the temperature T , for L = 8 , 16 , 32 , 64, and 128 and for (3 , 4 , 6 , 4) and (3 $^{4}$, 6) AL. FIG. 3: The susceptibility χ versus temperature T , for (3 , 4 , 6 , 4) and (3 $^{4}$, 6) AL. D$_{eff}$ = 1 . 82(4) for (3 , 4 , 6 , 4) and D$_{eff}$ = 1 . 64(5) for (3 $^{4}$, 6). The above results, indicate that the Ising S = 1 model on (3 , 4 , 6 , 4) and (3 $^{4}$, 6) AL does not fall in the same universality class as the square lattice Ising model, for which the critical exponents are known analytically i.e. β = 1 8 = 0 . 125, γ = 7 4 = 1 . 75 and ν = 1. We have checked numerically, that Ising S = 1 2 model repro- duces these critical exponents with reasonable accuracy for both studied lattices [25]. We improved the value of the critical temperature T$_{C}$ for these two lattices and S = 1 2 as well, with respect to Ref. [21]. Except the exponent ν , all critical exponents for S = 1 differ for more than three numerically estimated uncer- tainties from those given analytically. To obtain the critical exponent 1 /ν , we used the scaling relation (4). The calculated values of the exponents 1 /ν are 0 . 83(5) for (3 , 4 , 6 , 4) and 1 /ν = 0 . 94(5) for (3 $^{4}$, 6). Eq. (5) yields effective dimensionality of the systems Basing on the dependence ln χ on ln L we estimated γ/ν = 1 . 46(8) and γ/ν = 1 . 44(8) for (3 , 4 , 6 , 4) and (3 $^{4}$, 6) AL, respectively. In order to go further in our analysis we also com- puted the modulus of the magnetisation at the inflection M ∗ = M ( T$_{C}$ ). The estimated exponents β/ν values are 0 . 180(20) and 0 . 103(7) for (3 , 4 , 6 , 4) and (3 $^{4}$, 6) AL, re- spectively. In Fig. 4 the fourth-order Binder cumulant is shown as a function of the temperature for several values of L . Taking two largest lattices (for L = 64 and L = 128) we have T$_{C}$ = 1 . 590(3) and T$_{C}$ = 2 . 100(3) for (3 , 4 , 6 , 4) and (3 $^{4}$, 6) AL, respectively. In Fig. 3 the corresponding behaviour of the suscepti- bility χ is presented. The results are collected in Tab. I.