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.

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

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.

scholarly journals The bulk, surface and corner free energies of the anisotropic triangular Ising model

2020 ◽  
Vol 476 (2234) ◽  
pp. 20190713
Author(s):  
Rodney J. Baxter
Keyword(s):  
Free Energy ◽  
Ising Model ◽  
Partition Function ◽  
Temperature Series ◽  
Isotropic Case ◽  
Series Expansions ◽  
Exact Results ◽  
Free Energies ◽  
Bulk Surface ◽  
Bulk Free Energy

We consider the anisotropic Ising model on the triangular lattice with finite boundaries, and use Kaufman’s spinor method to calculate low-temperature series expansions for the partition function to high order. From these, we can obtain 108-term series expansions for the bulk, surface and corner free energies. We extrapolate these to all terms and thereby conjecture the exact results for each. Our results agree with the exactly known bulk-free energy and with Cardy and Peschel’s conformal invariance predictions for the dominant behaviour at criticality. For the isotropic case, they also agree with Vernier and Jacobsen’s conjecture for the 60 ° corners.

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