Finite-size scaling and the crossover to mean-field critical behavior in the two-dimensional Ising model with medium-ranged interactions

1993 ◽  
Vol 48 (4) ◽  
pp. 2498-2506 ◽  
Author(s):  
K. K. Mon ◽  
K. Binder
Keyword(s):  
Ising Model ◽  
Critical Behavior ◽  
Mean Field ◽  
Finite Size ◽  
Two Dimensional ◽  
Finite Size Scaling ◽  
Size Scaling

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

THE SIMULATION OF THE TWO-DIMENSIONAL ISING MODEL IN THE PRESENCE OF AN EXTERNAL MAGNETIC FIELD ON THE CREUTZ CELLULAR AUTOMATON

2000 ◽  
Vol 11 (03) ◽  
pp. 561-572 ◽  
Author(s):  
B. KUTLU ◽  
M. KASAP ◽  
S. TURAN
Keyword(s):  
Magnetic Field ◽  
Ising Model ◽  
External Magnetic Field ◽  
Cellular Automaton ◽  
Critical Behavior ◽  
Finite Size ◽  
Two Dimensional ◽  
Finite Size Scaling ◽  
Creutz Cellular Automaton ◽  
Good Agreement

The two-dimensional Ising model in a small external magnetic field, is simulated on the Creutz cellular automaton. The values of the static critical exponents for 0.0025 ≤ h ≤ 0.025 are estimated within the framework of the finite size scaling theory. The value of the field critical exponent is in a good agreement with its theoretical value of δ = 15. The results for 0.0025 ≤ h ≤ 0.025 are compatible with Ising critical behavior for T < Tc.

scholarly journals Anisotropic scaling of the two-dimensional Ising model I: the torus

2019 ◽  
Vol 7 (3) ◽  
Author(s):  
Hendrik Hobrecht ◽  
Fred Hucht
Keyword(s):  
Free Energy ◽  
Ising Model ◽  
Boundary Conditions ◽  
Scaling Limit ◽  
Finite Size ◽  
Square Lattice ◽  
Two Dimensional ◽  
Finite Size Scaling ◽  
Size Scaling ◽  
Anisotropic Scaling

We present detailed calculations for the partition function and the free energy of the finite two-dimensional square lattice Ising model with periodic and antiperiodic boundary conditions, variable aspect ratio, and anisotropic couplings, as well as for the corresponding universal free energy finite-size scaling functions. Therefore, we review the dimer mapping, as well as the interplay between its topology and the different types of boundary conditions. As a central result, we show how both the finite system as well as the scaling form decay into contributions for the bulk, a characteristic finite-size part, and – if present – the surface tension, which emerges due to at least one antiperiodic boundary in the system. For the scaling limit we extend the proper finite-size scaling theory to the anisotropic case and show how this anisotropy can be absorbed into suitable scaling variables.

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