Monte Carlo studies of finite-size scaling in the Gibbs ensemble at criticality for the two-dimensional Ising model

1993 ◽  
Vol 47 (9) ◽  
pp. 5497-5499 ◽  
Author(s):  
K. K. Mon
Keyword(s):  
Monte Carlo ◽  
Ising Model ◽  
Finite Size ◽  
Gibbs Ensemble ◽  
Two Dimensional ◽  
Finite Size Scaling ◽  
Size Scaling ◽  
Monte Carlo Studies

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

2009 ◽  
Vol 64 (12) ◽  
pp. 849-854 ◽  
Author(s):  
Ziya Merdan ◽  
Mehmet Bayirli ◽  
Mustafa Kemal Ozturk
Keyword(s):  
Critical Temperature ◽  
Ising Model ◽  
Specific Heat ◽  
Finite Size ◽  
Two Dimensional ◽  
Finite Size Scaling ◽  
Size Scaling ◽  
Infinite Lattice ◽  
Straight Line ◽  
Binder Parameter

The two-dimensional Ising model with nearest-neighbour pair interactions is simulated on 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 Tc = 2.287(6), Tc = 2.269(3), and Tc =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 (Tc =2.269) within the error limits. The values obtained for the critical exponent of the specific heat, α = 0.04(25) and α = 0.03(1), are in agreement with α = 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 Tc = 2.269(3) are calculated as gL(Tc) = −1.833(5), gL(Tc) = −1.834(3), gL(Tc) = −1.832(2), and gL(Tc) = −1.833(2), respectively. The value of the infinite lattice for the Binder parameter, gL(Tc) = −1.834(11), is obtained from the straight line fit of gL(Tc) = −1.833(5), gL(Tc) = −1.834(3), gL(Tc) = −1.832(2), and gL(Tc) = −1.833(2) versus L = 80, 120, 160, and 200, respectively

scholarly journals Finite size scaling analysis of intermittency moments in the two dimensional Ising model

1993 ◽  
Vol 314 (1) ◽  
pp. 74-78 ◽  
Author(s):  
Z. Burda ◽  
K. Zalewski ◽  
R. Peschanski ◽  
J. Wosiek
Keyword(s):  
Ising Model ◽  
Finite Size ◽  
Scaling Analysis ◽  
Two Dimensional ◽  
Finite Size Scaling ◽  
Size Scaling
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