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.

Exact high temperature series expansions for the XY model

1970 ◽  
Vol 48 (13) ◽  
pp. 1566-1577 ◽  
Author(s):  
D. D. Betts ◽  
C. J. Elliott ◽  
M. H. Lee
Keyword(s):  
High Temperature ◽  
Long Range ◽  
Lattice Gas ◽  
Critical Index ◽  
Temperature Series ◽  
Range Order ◽  
Xy Model ◽  
Long Range Order ◽  
Critical Temperatures ◽  
Quantum Lattice Gas

A method is developed for the exact high temperature series expansion of thermodynamic properties of the spin 1/2 XY model of ferromagnetism or of a quantum lattice gas. Eleven coefficients in the specific heat series for the f.c.c. and b.c.c. lattices and nine coefficients in the series for the fluctuation in the long range order for the f.c.c., b.c.c., and s.c. lattices are calculated. From the fluctuation series the critical temperatures Kc−1 ≡ kTc/J are estimated to be 4.520, 2.902, and 2.02 respectively, while the critical index for the square of the fluctuation in the long range order is γ = 1.35.

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.

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 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.

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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