Constraints on high-temperature series expansions for spin correlations in the square Ising model

1988 ◽  
Vol 37 (13) ◽  
pp. 7881-7883 ◽  
Author(s):  
J. O. Indekeu
Keyword(s):  
High Temperature ◽  
Ising Model ◽  
Temperature Series ◽  
Series Expansions ◽  
Spin Correlations

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.

Computer-aided generation of high-temperature series expansions for mixed-spin Ising model ferrimagnets

1995 ◽  
Vol 140-144 ◽  
pp. 1513-1514 ◽  
Author(s):  
G.J.A. Hunter ◽  
C.W. Evans ◽  
R.C.L. Jenkins ◽  
C.J. Tinsley ◽  
E.W. Wynn
Keyword(s):  
High Temperature ◽  
Ising Model ◽  
Temperature Series ◽  
Series Expansions ◽  
Mixed Spin ◽  
Computer Aided

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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