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.

Measurement of Long Range Order in the γ’ Phase of Nickel-Base Superalloys

1969 ◽  
Vol 13 ◽  
pp. 598-608
Author(s):  
J.R. Mihalisin
Keyword(s):  
High Temperature ◽  
Long Range ◽  
Range Order ◽  
Long Range Order ◽  
X Ray Diffraction ◽  
High Temperature Heat Treatment ◽  
Heat Treated ◽  
Temperature Heat ◽  
Long Time ◽  
Nickel Base

The long range order parameter (S) has been measured at room- temperature on the γ’ phase extracted from IN-731 and alloys 713C and 713LC by x-ray diffraction techniques. Measurements were obtained from specimens of IN-731 and alloy 713LC in the as-cast condition and after long time rupture testing. The alloy 713 c specimens were in the as-cast and high temperature heat treated conditions.It was found that long range order in the γ’ phase of IN-731 and alloy 713LC was changed very little after long time rupture testing, and after high temperature heat treatment in the case of alloy 713C.

Long-range order in the high-temperature phase ofK2ZnCl4

1997 ◽  
Vol 56 (9) ◽  
pp. 5180-5185 ◽  
Author(s):  
F. X. Leduc ◽  
A. Hedoux ◽  
M. Descamps ◽  
F. Danede ◽  
G. Odou
Keyword(s):  
High Temperature ◽  
Long Range ◽  
High Temperature Phase ◽  
Range Order ◽  
Temperature Phase ◽  
Long Range Order

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.

Sign in / Sign up

Export Citation Format

Share Document