Application of the Padé Approximant Method to the Investigation of Some Magnetic Properties of the Ising Model

1961 ◽  
Vol 124 (3) ◽  
pp. 768-774 ◽  
Author(s):  
George A. Baker
Keyword(s):  
Magnetic Properties ◽  
Ising Model ◽  
Padé Approximant ◽  
Pade Approximant ◽  
Approximant Method

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.

The rise of a cylindrical bubble in an inviscid liquid

1982 ◽  
Vol 60 (7) ◽  
pp. 999-1007 ◽  
Author(s):  
R. T. Baumel ◽  
S. K. Burley ◽  
D. F. Freeman ◽  
J. L. Gammel ◽  
J. Nuttall
Keyword(s):  
Gravitational Field ◽  
Padé Approximant ◽  
Inviscid Liquid ◽  
Pade Approximant ◽  
Approximant Method

An expansion in powers of t2 is obtained which gives the shape of an initially horizontal cylindrical bubble filled with a massless gas as it rises through an incompressible inviscid infinite fluid in a uniform vertical gravitational field. For larger times the series does not converge but we have found that a variation of the Padé approximant method gives good results for the locations of the top and bottom of the bubble, although not for times quite as large as might be desired. The results compare favourably with experiment.

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