A002917 High temperature series for spin-1/2 Ising specific heat on 3-dimensional b.c.c. lattice. (Formerly M3718 N1520)

4, 140, 4056, 129360, 4381848, 153700408, 5519859080, 201714989064

Offset

0,1

References

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Table of n, a(n) for n=0..7.

G. A. Baker, Further application of the Padé approximant method to the Ising and Heisenberg models, Phys. Rev. 129 (1963) 99-102.

Index entries for sequences related to b.c.c. lattice

Index entries for sequences related to specific heat

Formula

Sum_{n>=0} a(n) * v^(2*n) = (v^2-1) * (-q/2*f(v)^2 - (v^2-1) * f'(v)^2 + f(v) * (2*v*f'(v) + (v^2-1)*f''(v))) / f(v)^2, where f(v) = Sum_{n>=0} A001406(n) * v^(2*n) and q = 8 is the number of nearest neighbors. - Andrey Zabolotskiy, Feb 15 2022

Crossrefs

Cf. A002916 (cubic), A002918 (f.c.c.), A001406 (partition function), A047711 (internal energy), A002914 (susceptibility), A002167 (Heisenberg model).

Sequence in context: A093981 A055304 A270065 * A235536 A229453 A215606

Adjacent sequences: A002914 A002915 A002916 * A002918 A002919 A002920

Keyword

nonn,more

Author

N. J. A. Sloane

Extensions

Better description from Steven Finch

a(5)-a(7) from Andrey Zabolotskiy, Feb 15 2022

Status

approved