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

We investigate the critical properties of the Ising S=1/2 and S=1 model on(3,4,6,4)and(34,6)Archimedean lattices.The system is studied through the extensive Monte Carlo simulations.We calculate the critical temperature as well as the critical point exponentsγ/ν,β/ν,andνbasing on finite size scaling analysis.The calculated values of the critical temperature for S=1 are kBTC/J=1.590(3),and kBTC/J=2.100(4)for(3,4,6,4)and(34,6)Archimedean lattices,respectively.The critical exponentsβ/ν,γ/ν,and 1/ν,for S=1 areβ/ν=0.180(20),γ/ν=1.46(8),and 1/ν=0.83(5),for(3,4,6,4)and 0.103(8),1.44(8),and 0.94(5),for(34,6)Archimedean lattices.Obtained results differ from the Ising S=1/2 model on(3,4,6,4),(34,6)and square lattice.The evaluated effective dimensionality of the system for S=1 are Deff=1.82(4),for(3,4,6,4),and Deff=1.64(5)for(34,6).