The Finite-Size Scaling Study of the Ising Model for the Fractals

The fractals are obtained by using the model of diffusion-limited aggregation (DLA) for 40 ≤ L ≤ 240. The two-dimensional Ising model is simulated on the Creutz cellular automaton for 40 ≤ L ≤ 240. The critical exponents and the fractal dimensions are computed to be β = 0.124(8), γ = 1.747(10), α = 0.081(21), δ = 14.994(11), η = 0.178(10), ν = 0.960(23) and d_f^{β } =1.876(8), d_f^{γ } =3.747(10), d_f^{α } =2.081(68), d_f^{δ } =1.940(22), d_f^{η } =2.178(10), d_f^{ν } =2.960(22), which are consistent with the theoretical values of β = 0.125, γ = 1.75, α = 0, δ = 15, η = 0.25, ν = 1 and d_f^{β } =1.875, d_f^{γ } =3.75, d_f^{α } =2, d_f^{δ } =1.933, d_f^{η } =2.25, d_f^{ν } =3.