The spin XY model. V. Moments of the spin–spin correlations in three dimensions

1980 ◽  
Vol 58 (11) ◽  
pp. 1651-1657 ◽  
Author(s):  
D. D. Betts ◽  
E. W. Grundke
Keyword(s):  
High Temperature ◽  
Three Dimensions ◽  
Transverse Spin ◽  
Xy Model ◽  
Spin Correlations ◽  
Cubic Lattices ◽  
Simple Cubic ◽  
Text Model ◽  
Critical Amplitudes

Ninth degree high temperature expansions have been obtained for all transverse spin–spin correlations of the [Formula: see text] model on the simple cubic and body centred cubic lattices. Analysis of the series for the second and fourth moments of the correlations yields the estimate of v = 0.689 ± 0.010 and estimates of critical amplitudes. No evidence for violation of hyperscaling is found.

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.

scholarly journals High-temperature Thermodynamics of the Hubbard Model

1993 ◽  
Vol 46 (5) ◽  
pp. 613
Author(s):  
J Oitmaa ◽  
JA Henderson
Keyword(s):  
High Temperature ◽  
Hubbard Model ◽  
Specific Heat ◽  
High Temperatures ◽  
Padé Approximants ◽  
Numerical Results ◽  
Strongly Correlated ◽  
Cubic Lattices ◽  
Simple Cubic ◽  
Atomic Limit

Recently derived 10th-order high-temperature expansions for the Hubbard model are used to obtain the ferromagnetic susceptibility and specific heat at high temperatures. Numerical results are obtained for the simple cubic and face-centred cubic lattices by using Pade approximants to sum the series. The results are compared with two solvable limiting cases, namely the non-interacting limit U = 0 and the strongly-correlated or atomic limit t = O.

Application of the Green Function Method to the XY Model in a Magnetic Field

1974 ◽  
Vol 52 (17) ◽  
pp. 1660-1665 ◽  
Author(s):  
D. J. Austen
Keyword(s):  
Magnetic Field ◽  
Green Function ◽  
Three Dimensions ◽  
Xy Model ◽  
Zero Field ◽  
Green Function Method ◽  
Function Solution ◽  
Cubic Lattices ◽  
The Green Function ◽  
Improved Accuracy

This paper exhibits a simple, approximate Green function solution for the XY model of ferromagnetism in three dimensions from which we obtain the critical temperature, magnetization, internal energy, free energy, and entropy as a function of a magnetic field in the z direction. Comparison with Padé analysis of known high temperature series indicates an accuracy for TC in zero field to within 2% on all three cubic lattices and improved accuracy for nonzero fields. Solutions are obtained only for T ≥ TC.

High-temperature properties of the Ising model on the cristobalite lattice

1968 ◽  
Vol 46 (8) ◽  
pp. 971-975 ◽  
Author(s):  
D. D. Betts ◽  
R. V. Ditzian
Keyword(s):  
High Temperature ◽  
Ising Model ◽  
Curie Temperature ◽  
Coordination Number ◽  
Critical Energy ◽  
Critical Parameters ◽  
High Temperature Properties ◽  
Cubic Lattices ◽  
Simple Cubic ◽  
Effect Of Structure

The high-temperature properties of the Ising model on the cristobalite lattice are investigated by series expansion methods. The Curie temperature is found to be vl = tanh J/kTl = 0.2330 ± 0.003, the amplitude of the singularity in the susceptibility is Γ = 1.100 ± 0.001, the critical energy is −Ec/kTc = 0.268 ± 0.006, and the critical entropy is Sc/k = 0.548 ± 0.003. A comparison of critical parameters for the cristobalite and simple cubic lattices allows one to see the effect of structure for two lattices of the same coordination number.

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