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

Abstract

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 exponents γ/ν, β/ν, and ν 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 (3⁴,6) Archimedean lattices, respectively. The critical exponents β/ν, γ/ν, and 1/ν, for S=1 are β/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 D_eff =1.82(4), for (3,4,6,4), and D_eff=1.64(5) for (3⁴,6).