Finite-size scaling and the convective conductance and specific heat of planar helium films near the superfluid transition

1989 ◽  
Vol 39 (10) ◽  
pp. 6519-6526 ◽  
Author(s):  
Y. Y. Yu ◽  
D. Finotello ◽  
F. M. Gasparini
Keyword(s):  
Specific Heat ◽  
Finite Size ◽  
Superfluid Transition ◽  
Finite Size Scaling ◽  
Helium Films ◽  
Size Scaling

A FINITE-SIZE SCALING STUDY OF THE FOUR-DIMENSIONAL ISING MODEL ON THE CREUTZ CELLULAR AUTOMATON

1999 ◽  
Vol 10 (05) ◽  
pp. 875-881 ◽  
Author(s):  
N. AKTEKIN ◽  
A. GÜNEN ◽  
Z. SAĞLAM
Keyword(s):  
Magnetic Susceptibility ◽  
Ising Model ◽  
Cellular Automaton ◽  
Specific Heat ◽  
Finite Size ◽  
Scaling Relations ◽  
Finite Size Scaling ◽  
Critical Temperatures ◽  
Size Scaling ◽  
Creutz Cellular Automaton

The four-dimensional Ising model is simulated on the Creutz cellular automaton with increased precision. The data are analyzed according to the finite-size scaling relations available. The precision of the critical values related to magnetic susceptibility is improved by one digit, but in order to reach to the same precision for those related to the specific heat more simulation runs at the critical temperatures of the finite-size lattices are required.

Publisher's Note: Finite-size scaling ofHe4at the superfluid transition [Rev. Mod. Phys. 80, 1009 (2008)]

2008 ◽  
Vol 80 (3) ◽  
pp. 1195-1195
Author(s):  
Francis M. Gasparini ◽  
Mark O. Kimball ◽  
Kevin P. Mooney ◽  
Manuel Diaz-Avila
Keyword(s):  
Finite Size ◽  
Superfluid Transition ◽  
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

THE FINITE-SIZE SCALING STUDY OF THE SPECIFIC HEAT AND THE BINDER PARAMETER FOR THE 7-DIMENSIONAL ISING MODEL

2007 ◽  
Vol 21 (04) ◽  
pp. 215-224 ◽  
Author(s):  
Z. MERDAN ◽  
D. ATILLE
Keyword(s):  
Critical Temperature ◽  
Ising Model ◽  
Cellular Automaton ◽  
Specific Heat ◽  
Finite Size ◽  
Finite Size Scaling ◽  
Size Scaling ◽  
Infinite Lattice ◽  
Creutz Cellular Automaton ◽  
Binder Parameter

The 7-dimensional Ising model with nearest-neighbor pair interactions is simulated on the Creutz cellular automaton by using the finite-size lattices with the linear dimensions L = 4, 6, 8. The temperature variations and the finite-size scaling plots of the specific heat and 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 = 12.866(2), T c = 12.871(2) and T c = 12.871(49) 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 more precise values of the Creutz cellular automaton results of T c = 12.8700(42), the 1/d-expansion result of T c = 12.8712, the series expansion result of T c = 12.86902(33), the dynamic Monte Carlo result of T c = 12.8667(50). The values obtained for the critical exponent of the specific heat, i.e., α = 0.011(76), α = -0.002, α = 0.011(5) and α = 0.082(32) corresponding to the above T c values, respectively, are in agreement with α = 0 predicted by the theory. Moreover the values for the Binder parameter are calculated as gL(T c ) = -1.022(28), gL(T c ) = -1.09, gL(T c ) = -1.01(12) and gL(T c ) = -1.34(55) corresponding to the above T c values, respectively.

THE FINITE-SIZE SCALING STUDY OF THE SPECIFIC HEAT AND THE BINDER PARAMETER FOR THE FIVE-DIMENSIONAL ISING MODEL

2007 ◽  
Vol 21 (28) ◽  
pp. 1923-1931 ◽  
Author(s):  
M. KALAY ◽  
Z. MERDAN
Keyword(s):  
Critical Temperature ◽  
Ising Model ◽  
Specific Heat ◽  
Nearest Neighbor ◽  
Finite Size ◽  
Finite Size Scaling ◽  
Size Scaling ◽  
Infinite Lattice ◽  
Creutz Cellular Automaton ◽  
Binder Parameter

The five-dimensional Ising model with nearest-neighbor pair interactions is simulated on the Creutz cellular automaton by using finite-size lattices with the linear dimensions L=4, 6, 8, 10, 12, 14, and 16. The temperature variations and the finite-size scaling plots of the specific heat and 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 =8.8063, T c =8.7825 and T c =8.7572, 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 more precise value of T c =8.7787. The value obtained for the critical exponent of the specific heat, i.e. α=0.009, is also in agreement with α=0 predicted by the theory.

Finite-size scaling of the specific heat of4 He near Tλ

1994 ◽  
Vol 194-196 ◽  
pp. 611-612 ◽  
Author(s):  
Andreas Wacker ◽  
Volker Dohm
Keyword(s):  
Specific Heat ◽  
Finite Size ◽  
Finite Size Scaling ◽  
Size Scaling
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