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    The Finite-Size Scaling Study of the Specific Heat and the Binder Parameter of the Two-Dimensional Ising Model for the Fractals Obtained by Using the Model of Diffusion-Limited Aggregation
    (Walter De Gruyter Gmbh, 2009) Merdan, Ziya; Bayırlı, Mehmet; Özturk, Mustafa Kemal
    The two-dimensional Ising model with nearest-neighbour pair interactions is simulated oil the Creutz cellular automaton by using the finite-size lattices with the linear dimensions L = 80, 120, 160, and 200. The temperature variations and the finite-size scaling plots of the specific heat and the Binder parameter verify the theoretically predicted expression near the infinite lattice critical temperature. The approximate values for the critical temperature of the infinite lattice T-c = 2.287(6) T-c = 2.269(3), and T-c =2.271(1) are obtained from the intersection points of specific heat curves. Binder parameter curves, and the straight line fit of specific heat maxima, respectively. These results are in agreement with the theoretical value (T-c =2.269) within the error limits. The values obtained for the critical exponent of the specific heat, alpha = 0.04(25) and alpha = 0.03(l), are in agreement with alpha = 0 predicted by the theory. The values for the Binder parameter by using the finite-size lattices with the linear dimension L = 80, 120, 160, and 200 at T-c = 2.269(3) are calculated as g(L)(T-c) = -1.833(5), g(L)(T-c) = -1.834(3), g(L)(T-c) = -1.832(2), and g(L)(T-c) = -1.833(2), respectively. The value of the infinite lattice for the Binder parameter, g(L)(T-c) = -1.834(11), is obtained from the straight line fit of g(L)(T-c) = -1.833(5), g(L)(T-c) = -1.834(3), g(L)(T-c) = -1.832(2), and g(L)(T-c) = -1.833(2) versus L = 80, 120, 160, and 200, respectively.
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    The Simulation of the Two-Dimensional Ising Model on the Creutz Cellular Automaton for the Fractals Obtained by Using the Model of Diffusion-Limited Aggregation
    (Walter De Gruyter Gmbh, 2010) Merdan, Ziya; Bayırlı, Mehmet; Öztürk, Mustafa Kemal
    The fractals are obtained by using the model of diffusion limited aggregation (DLA) for the lattice with L = 80 120, and 160 The values of the fractal dimensions are compared with the results of former studies As increasing the linear dimensions they are in good agreement with those The fractals obtained by using the model of DLA rue simulated on the Creutz cellular automaton by using a two bit demon The values computed for the critical temperature and the static critical exponents within the framework of the brute size scaling theory are in agreement with the results of other simulations and theoretical values