Properties of a Lattice Gas Model for 3He–4He Mixtures II: Analysis of High Temperature Series for the f.c.c. Lattice

1975 ◽  
Vol 53 (10) ◽  
pp. 987-1002 ◽  
Author(s):  
M. Plischke ◽  
D. D. Betts
Keyword(s):  
High Temperature ◽  
Specific Heat ◽  
Lattice Gas ◽  
Chemical Potential ◽  
Constant Pressure ◽  
Temperature Series ◽  
Adjustable Parameter ◽  
Constant Density ◽  
Constant Concentration ◽  
Chemical Potential Difference

For the Cheng–Schick model of 3He–4He mixtures high temperature series expansions at (a) constant density and constant concentration and (b) constant pressure and constant chemical potential difference are presented for the f.c.c. lattice for the fluctuation in the superfluid order parameter, the concentration susceptibility, and the specific heat at constant chemical potential. Analysis of the fluctuation series yields well defined lambda temperatures. In addition analysis of the concentration susceptibility series provides a less precise estimate of the tricritical concentration. The specific heat series have not proved very amenable to analysis. Upon fixing a single adjustable parameter the lambda curve of the model agrees precisely with experiment for all 3He concentrations. Estimates of tricritical exponents could not be obtained.

Reliability Implications of Defects in High Temperature Annealed Si/SiO2/Si Structures

1994 ◽  
Vol 338 ◽  
Author(s):  
W. L. Warren ◽  
D. M. Fleetwood ◽  
M. R. Shaneyfelt ◽  
P. S. Winokur ◽  
R. A. B. Devine ◽  
...  
Keyword(s):  
High Temperature ◽  
Chemical Potential ◽  
Field Effect Transistors ◽  
Radiation Sensitivity ◽  
Oxide Semiconductor ◽  
Interfacial Region ◽  
Si Substrate ◽  
Paramagnetic Defect ◽  
Chemical Potential Difference ◽  
Hole Trapping

ABSTRACTHigh-temperature post-oxidation annealing of poly-Si/SiO2/Si structures such as metal-oxidesemiconductor capacitors and metal-oxide-semiconductor field effect transistors is known to result in enhanced radiation sensitivity, increased 1/f noise, and low field breakdown. We have studied the origins of these effects from a spectroscopic standpoint using electron paramagnetic resonance (EPR) and atomic force microscopy. One result of high temperature annealing is the generation of three types of paramagnetic defect centers, two of which are associated with the oxide close to the Si/SiO2 interface (oxygen-vacancy centers) and the third with the bulk Si substrate (oxygen-related donors). In all three cases the origin of the defects may be attributed to out-diffusion of O from the SiO2 network into the Si substrate with associated reduction of the oxide. We present a straightforward model for the interfacial region which assumes the driving force for O out-diffusion is the chemical potential difference of the O in the two phases (SiO2 and the Si substrate). Experimental evidence is provided to show that enhanced hole trapping and interface-trap and border-trap generation in irradiated high-temperature annealed Si/SiO2/Si systems are all related either directly, or indirectly, to the presence of oxygen vacancies.

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.

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

FIRST SOUND IN LIQUID HELIUM AT HIGH PRESSURES

1953 ◽  
Vol 31 (7) ◽  
pp. 1156-1164 ◽  
Author(s):  
K. R. Atkins ◽  
R. A. Stasior
Keyword(s):  
Specific Heat ◽  
Liquid Helium ◽  
Carrier Frequency ◽  
High Pressures ◽  
Constant Pressure ◽  
Constant Density ◽  
Pulse Technique ◽  
Temperature Range ◽  
Specific Heats ◽  
First Sound

The velocity of ordinary sound in liquid helium has been measured in the temperature range from 1.2 °K. to 4.2 °K. at pressures up to 69 atm. A pulse technique was used with a carrier frequency of 12 Mc.p.s. Curves are given for the variation of velocity with temperature at constant pressure and also at constant density. There is no detectable discontinuity along the λ-curve. The results are used to discuss the ratio of the specific heats, the coefficient of expansion below 0.6 °K., and the specific heat above 3 °K.

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.

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.

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.

Analysis of the specific heat of body-centred cubic 3He in a high magnetic field using high-temperature series expansion with a multiple-exchange Hamiltonian

1987 ◽  
Vol 65 (11) ◽  
pp. 1539-1542
Author(s):  
E. Suaudeau ◽  
M. Roger ◽  
M. E. R. Bernier
Keyword(s):  
High Temperature ◽  
Specific Heat ◽  
Series Expansion ◽  
Temperature Series ◽  
The Body ◽  
Cubic Phase ◽  
High Magnetic Fields ◽  
Multiple Exchange ◽  
Particle Exchange ◽  
Order Four

We have extended to order four in β = 1/kBT the high-temperature series expansion for the body-centred cubic phase of solid 3He with a Hamiltonian including two-, three-, and four-particle exchange. The results are used to analyze recent experimental measurements of the specific heat at low temperature and high magnetic fields.

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