The finite-size scaling study of the ising model for the fractals

Abstract

The fractals are obtained by using the model of diffusion-limited aggregation (DLA) for 40 a parts per thousand currency sign L a parts per thousand currency sign 240. The two-dimensional Ising model is simulated on the Creutz cellular automaton for 40 a parts per thousand currency sign L a parts per thousand currency sign 240. The critical exponents and the fractal dimensions are computed to be beta = 0.124(8), gamma = 1.747(10), alpha = 0.081(21), delta = 14.994(11), eta = 0.178(10), nu = 0.960(23) and , , , which are consistent with the theoretical values of beta = 0.125, gamma = 1.75, alpha = 0, delta = 15, eta = 0.25, nu = 1 and .