FWSL acknowledges the Brazilian agency FAPEPI (Teresina, Piau´ı, Brazil) for its financial support. This work also was supported (in part) from the AGH-UST project 11.11.220.01. Part of the calculations was car- ried out on SGI Altix 1350 system at the computational park CENAPAD.UNICAMP-USP, S˜ ao Paulo, Brazil and on SGI Altix 3700 system at Academic Computer Centre Cyfronet-AGH in Cracow, Poland. Acknowledgments 4 -1  0  1  2  3  4  5  6  7  8  9  10  1.52  1.54  1.56  1.58  1.6  1.62  1.64  1.66 8 16 32 64 128 k B T/J L = − ln(1 − 3 U/ 2) (3 , 4 , 6 , 4) -1  0  1  2  3  4  5  6  7  8  9  10  2.02  2.04  2.06  2.08  2.1  2.12  2.14  2.16  2.18 8 16 32 64 128 PS f rag rep laceme n ts k B T/J L = − ln(1 − 3 U/ 2) (3 , 4 , 6 , 4) (3 $^{4}$, 6) S k B T C /J β/ν γ/ν 1 /ν D eff (3 , 4 , 6 , 4) 1 1.590(3) 0.180(20) 1.46(8) 0.83(5) 1.82(4) (3 $^{4}$, 6) 1 2.100(3) 0.103(8) 1.44(8) 0.94(5) 1.64(5) (3 , 4 , 6 , 4) 1 2 2.145(3) 0.123(17) 1.680(74) 1.066(44) 1.926(84) (3 $^{4}$, 6) 1 2 2.784(3) 0.113(10) 1.726(8) 1.25(13) 1.952(22) square (4 $^{4}$) 1 2 2 / arcsinh(1) 1 8 7 4 1 2 FIG. 4: The reduced Binder’s fourth-order cumulant U as a function of the temperature T , for (3 , 4 , 6 , 4) and (3 $^{4}$, 6) AL. TABLE I: Critical points and critical points exponents for (3 , 4 , 6 , 4) and (3 $^{4}$, 6) AL. For comparison, the exact values for the square lattice Ising S = 1 2 model are included as well. [1] W. Lenz, Z. Phys. 21 , 613 (1920). [2] E. Ising, Z. Phys. 31 , 253 (1925). [3] R. B. Potts, Proc. Cambridge Phil. Soc. 48 , 106 (1952). [4] Fa-Yueh Wu, Rev. Mod. Phys. 54 235 (1982). [5] M. Blume, Phys. Rev. 141 , 517 (1966). [6] H. W. Capel, Physica (Amsterdam) 32 , 966 (1966). [7] D. M. Saul, M. Wortis, D. Staufer, Phys. Rev. B 9 , 4964 (1974). [8] A. K. Jain, D. P. Landau, Phys. Rev. B 22 , 445 (1980). [9] O. F. de Alcantara Bonfim, Physica A 130 , 367 (1985). [10] A. N. Berker, M. Wortis, Phys. Rev. B 14 , 4946 (1976). [11] S. Moss de Oliveira, P. M. C. de Oliveira, F. C. S´ a Bar- reto, J. Stat. Phys. 78 , 1619 (1995). [12] J. A. Plascak, J. G. Moreira, F. C. S´ a Barreto, Phys. Lett. A 173 , 360 (1993). [13] M. N. Tamashiro, S. R. Salinas, Physica A 211 , 124 (1994). [14] J. C. Xavier, F. C. Alcaraz, D. Pe˜ na Lara, J. A. Plascak, Phys. Rev. B 57 , 11575 (1998). [15] D. Pe˜ na Lara, J. A. Plascak, Int. J. Mod. Phys. B 12 , [16] F. C. S´ a Barreto, O. F. Alcantara Bonfim, Physica A 172 , 378 (1991). [17] A. Bakchinch, A. Bassir, A. Benyoussef, Physica A 195 , 188 (1993). [18] J. A. Plascak, D. P. Landau, Phys. Rev. E 67 , R015103 (2003). [19] F. W. S. Lima, Int. J. Mod. Phys. C 17 , 1267 (2006). [20] P. N. Suding, R. M. Ziff, Phys. Rev. E 60 , 275 (1999) [21] K. Malarz, M. Zborek, B. Wr´ obel, TASK Quartely 9 , 475 (2005). [22] F. W. S. Lima, K. Malarz, Int. J. Mod. Phys. C 17 , 1273 (2006). [23] D. P. Landau, K. Binder, A Guide to Monte Carlo Sim- ulations in Statistical Physics , 2nd edition, Cambridge UP, 2005. [24] K. Binder, Z. Phys. B 43 , 119 (1981). [25] J. Mostowicz, M.Sc. Thesis, AGH-UST, Krak´ ow (2009). 2045 (1998).