Regularly spaced blocks of impurities in the Ising model: Critical temperature and specific heat

1977 ◽  
Vol 15 (11) ◽  
pp. 5391-5411 ◽  
Author(s):  
John R. Hamm
Keyword(s):  
Critical Temperature ◽  
Ising Model ◽  
Specific Heat

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.

High-temperature properties of the Ising model on the octahedral lattice

1970 ◽  
Vol 48 (20) ◽  
pp. 2383-2390 ◽  
Author(s):  
J. Oitmaa ◽  
C. J. Elliott
Keyword(s):  
High Temperature ◽  
Critical Temperature ◽  
Ising Model ◽  
Specific Heat ◽  
Reliable Estimate ◽  
Series Expansions ◽  
High Temperature Properties ◽  
Initial Susceptibility

The high-temperature initial susceptibility and specific heat of the spin 1/2 Ising model on the octahedral lattice are investigated by the method of exact series expansions. From the susceptibility series the critical temperature is found to be νc = tanh J/kTc = 0.1613 ± 0.0001. By using a method due to Gibberd the specific-heat series is calculated to 15 terms but a reliable estimate of the exponent a is not obtained, although the results do support the presently believed value α = 1/8.

BOSE–EINSTEIN STATISTICS IN A DISCRETE SPECTRUM TRAP

2004 ◽  
Vol 18 (04n05) ◽  
pp. 555-563 ◽  
Author(s):  
ENRICO CELEGHINI ◽  
MARIO RASETTI
Keyword(s):  
Critical Temperature ◽  
Low Temperature ◽  
Specific Heat ◽  
Discrete Spectrum ◽  
Harmonic Trap ◽  
Statistical Properties ◽  
Bose Einstein ◽  
The Continuum

A detailed description of the statistical properties of a system of bosons in a harmonic trap at low temperature, which is expected to bear on the process of BE condensation, is given resorting only to the basic postulates of Gibbs and Bose, without assuming equipartition nor continuum statistics. Below Tc such discrete spectrum theory predicts for the thermo-dynamical variables a behavior different from the continuum case. In particular a new critical temperature Td emerges where the specific heat exhibits a λ-like spike.

scholarly journals The atomic rearrangement process in the copper-gold alloy Cu 3 Au

1936 ◽  
Vol 157 (890) ◽  
pp. 213-233 ◽  
Keyword(s):  
Critical Temperature ◽  
Specific Heat ◽  
High Temperatures ◽  
Energy Content ◽  
Relative Number ◽  
Local Order ◽  
Total Change ◽  
High Specific Heat ◽  
Degree Of Order ◽  
Atomic Rearrangement

When certain single-phase alloys are cooled from high temperatures they undergo transformations consisting of a change from a random distribution of atoms amongst the atomic sites to an ordered one. The thermodynamics of such transformations have been considered by Bragg and Williams and also by Bethe and Peierls; the former assume that the energy involved in any atomic interchange is directly proportional to the statistical degree of order (superlattice order) throughout the whole alloy crystal, whilst the latter consider that it depends only on the relative number of like and unlike atoms immediately surrounding the atoms concerned in the interchange (order of nearest neighbours). Both assumptions enable relations to be derived for the change in degree of order (as separately defined) with temperature under equilibrium conditions. These relations are then used to calculate the change in energy content produced as a result of the atomic rearrangement. According to the theory of Bragg and Williams, the superlattice order disappears entirely on heating the alloy through the critical temperature and the energy content is affected only by the ordering process below the critical temperature. The theory of Bethe predicts that, although superlattice order disappears at the critical temperature, a high degree of local order persists, which vanishes only at very high temperatures; an abnormally high specific heat is to be expected, therefore, even above the critical temperature. In the case of β brass (CuZn) both theories give practically the same result for the total change in internal energy below the critical temperature, which is in reasonable agreement with experimental measurement. Neither theory gives the correct rate of release of energy in the neighbourhood of the critical temperature, and it would appear that the final disappearance of superlattice order is more sudden than theory indicates. The specific heat is abnormally high above the critical temperature owing presumably to the presence of local order.

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