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.

High-temperature specific heat series of the Ising model on the crystobalite lattice

1970 ◽  
Vol 48 (3) ◽  
pp. 307-312 ◽  
Author(s):  
R. W. Gibberd
Keyword(s):  
High Temperature ◽  
Ising Model ◽  
Partition Function ◽  
Specific Heat ◽  
Temperature Series ◽  
Padé Approximant ◽  
Reliable Estimate ◽  
Pade Approximant

Betts and Ditzian have recently published the first 11 coefficients of the exact high-temperature series for the specific heat of the spin 1/2 Ising model on a crystobalite lattice. In this paper the exact coefficients for the next 8 terms are derived by making use of an approximate transformation between the Ising partition function of the crystobalite and diamond lattices. The series is analyzed by using the ratio and Padé approximant methods, but a reliable estimate for α has not been obtained.

Logarithmic Factors, Critical Temperature, and Zero Temperature Flipping in the 4D Kinetic Ising Model

1997 ◽  
Vol 08 (02) ◽  
pp. 263-267 ◽  
Author(s):  
Dietrich Stauffer ◽  
Joan Adler
Keyword(s):  
Critical Temperature ◽  
Ising Model ◽  
Nearest Neighbor ◽  
Kinetic Monte Carlo ◽  
Series Expansions ◽  
Fourth Moment ◽  
Zero Temperature ◽  
Kinetic Ising Model ◽  
Kinetic Monte Carlo Simulations ◽  
Error Bars

We determine the critical temperature in the four-dimensional nearest-neighbor Ising model as J/kB Tc=0.149694±0.000002 from kinetic Monte Carlo simulations of up to 5764 spins. Here we assume the critical magnetization to decay with time as (t/ log t)-1/2. However, possible logarithmic additions to this leading scaling behavior could change the estimate beyond these error bars. A reanalyzis of old series expansions for the susceptibility and fourth moment gives 0.149696±0.000004.

scholarly journals Specific-heat exponent for the three-dimensional Ising model from a 24th-order high-temperature series

1994 ◽  
Vol 49 (18) ◽  
pp. 12909-12914 ◽  
Author(s):  
Gyan Bhanot ◽  
Michael Creutz ◽  
Uwe Glässner ◽  
Klaus Schilling
Keyword(s):  
High Temperature ◽  
Ising Model ◽  
Specific Heat ◽  
Three Dimensional ◽  
Temperature Series

The spin model. III. Analysis of high temperature series expansions of some thermodynamic quantities in two dimensions

1979 ◽  
Vol 57 (10) ◽  
pp. 1719-1730 ◽  
Author(s):  
J. Rogiers ◽  
E. W. Grundke ◽  
D. D. Betts
Keyword(s):  
High Temperature ◽  
Specific Heat ◽  
Spin Model ◽  
Two Dimensions ◽  
Temperature Series ◽  
Transverse Spin ◽  
Series Expansions ◽  
Xy Model ◽  
Thermodynamic Quantities ◽  
Spin Correlations

In this paper we report analyses of high temperature series expansions for the spin [Formula: see text] XY model on the triangular and square lattices. Quantities for which series are analyzed include the fluctuation in the transverse magnetization, fourth order fluctuations in the same quantity, second and fourth moments of the transverse spin–spin correlations, specific heat, and entropy. The evidence favours a phase transition at a finite temperature with conventional power law critical singularities. Scaling seems to hold but hyperscaling seems to be violated. Estimates for critical exponents include γ = 2.50 ± 0.3. Δ = 2.38 ± 0.2, and ν = 143 ± 0.10. The specific heat exhibits no singular behaviour at Tc.

Sign in / Sign up

Export Citation Format

Share Document