The spin model. I. Derivation of high temperature series expansions for thermodynamic quantities

1978 ◽  
Vol 56 (4) ◽  
pp. 409-419 ◽  
Author(s):  
J. Rogiers ◽  
T. Lookman ◽  
D. D. Betts ◽  
C. J. Elliott
Keyword(s):  
Free Energy ◽  
High Temperature ◽  
Fourth Order ◽  
Spin Model ◽  
Temperature Series ◽  
Transverse Magnetization ◽  
Series Expansions ◽  
Thermodynamic Quantities ◽  
Inverse Temperature ◽  
Text Model

Exact high temperature series expansions have been obtained for the free energy, the fluctuation of the transverse magnetization, and the fourth order fluctuation of the transverse magnetization of the spin [Formula: see text] model through degrees 13, 12, and 9, respectively, in the inverse temperature on one, two, three, and four dimensional lattices. A new method for identifying graphs and a new theorem for calculating vertical weights have been introduced in this work.

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.

The spin XY model. IV. Analysis of high temperature series expansions of some thermodynamic quantities in four dimensions

1980 ◽  
Vol 58 (1) ◽  
pp. 87-93
Author(s):  
J. Rogiers
Keyword(s):  
High Temperature ◽  
Order Parameter ◽  
Temperature Series ◽  
Series Expansions ◽  
Xy Model ◽  
Logarithmic Correction ◽  
Thermodynamic Quantities ◽  
Four Dimensions ◽  
Hypercubic Lattice ◽  
The Face

The series for the fluctuation of the order parameter and the fourth-order fluctuation of the order parameter of the S = [Formula: see text] XY model on four-dimensional lattices are analysed. Assuming a simple power law we find γ = 1.125 ± 0.010 for the simple hypercubic and γ = 1.113 ± 0.005 for the face-centred hypercubic. An alternative method of analysis which includes a logarithmic correction factor and assumes γ = 1 gives as power for the logarithmic correction p = 0.36 ± 0.05 for the simple hypercubic lattice.

Properties of a Lattice Gas Model for 3He–4He Mixtures I: Generation of High Temperature Series

1975 ◽  
Vol 53 (10) ◽  
pp. 980-986 ◽  
Author(s):  
M. Plischke ◽  
C. J. Elliott
Keyword(s):  
High Temperature ◽  
Lattice Gas ◽  
Temperature Series ◽  
Quantum Mechanical ◽  
Series Expansions ◽  
Xy Model ◽  
Exchange Constant ◽  
Inverse Temperature ◽  
Lattice Fluid ◽  
Special Case

The Cheng–Schick model is a quantum mechanical lattice fluid for 3He–4He mixtures which reduces in one limit to the spin 1/2 XY model and in the opposite limit to a special case of the Hubbard model. The method for generating high temperature series expansions of the thermodynamic properties of the model is described in some detail. Series expansions in the inverse temperature have been obtained to order 10 for the free energy and to order 8 for the fluctuation in the long range order both for arbitrary boson and fermion fugacities and arbitrary exchange constant ratios. In the following article (Plischke and Betts) the series are analyzed and the results are compared with experiment and with other theories for 3He–4He mixtures.

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.

Effect of Zn Substitution on Magnetic Properties of CuFe 2 O 4 : a High-Temperature Series Expansions Study

2018 ◽  
Vol 35 (1) ◽  
pp. 017501 ◽  
Author(s):  
S. Salmi ◽  
R. Masrour ◽  
A. El Grini ◽  
K. Bouslykhane ◽  
A. Hourmatallah ◽  
...  
Keyword(s):  
Magnetic Properties ◽  
High Temperature ◽  
Temperature Series ◽  
Series Expansions ◽  
Zn Substitution
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