Commun. Comput. Phys., 10 (2011), pp. 912-919. Critical Behaviour of the Ising S=1/2 and S=1 Model on (3,4,6,4) and (3,3,3,3,6) Archimedean Lattices F. W. S. Lima 1*, J. Mostowicz 2, K. Malarz 21 Dietrich Stauffer Computational Physics Lab, Departamento de Fisica, Universidade Federal do Piaui, 64049-550 Teresina, Piaui, Brazil. 2 Faculty of Physics and Applied Computer Science, AGH University of Science and Technology, al. Mickiewicza 30, PL-30059 Krakow, Poland. Received 9 September 2010; Accepted (in revised version) 2 December 2010 Available online 13 June 2011 doi:10.4208/cicp.090910.021210a Abstract We investigate the critical properties of the Ising $S=1/2$ and $S=1$ model on $(3,4,6,4)$ and $(3^4,6)$ Archimedean lattices. The system is studied through the extensive Monte Carlo simulations. We calculate the critical temperature as well as the critical point exponents $\gamma/\nu$, $\beta/\nu$, and $\nu$ basing on finite size scaling analysis. The calculated values of the critical temperature for $S=1$ are $k_BT_C/J=1.590(3)$, and $k_BT_C/J=2.100(4)$ for $(3,4,6,4)$ and $(3^4,6)$ Archimedean lattices, respectively. The critical exponents $\beta/\nu$, $\gamma/\nu$, and $1/\nu$, for $S=1$ are $\beta/\nu=0.180(20)$, $\gamma/\nu=1.46(8)$, and $1/\nu=0.83(5)$, for $(3,4,6,4)$ and $0.103(8)$, $1.44(8)$, and $0.94(5)$, for $(3^4,6)$ Archimedean lattices. Obtained results differ from the Ising $S=1/2$ model on $(3,4,6,4)$, $(3^4,6)$ and square lattice. The evaluated effective dimensionality of the system for $S=1$ are $D_{\text{eff}}=1.82(4)$, for $(3,4,6,4)$, and $D_{\text{eff}}=1.64(5)$ for $(3^4,6)$. Notice: Undefined variable: ams in /var/www/html/issue/abstract/readabs.php on line 163 PACS: 05.70.Ln, 05.50.+q, 75.40.Mg, 02.70.Lq Key words: Monte Carlo simulation, Ising model, critical exponents. *Corresponding author. Email: fwslima@gmail.com (F. W. S. Lima), mostowicz@gmail.com (J. Mostowicz), malarz@agh.edu.pl (K. Malarz)