A047712 High-temperature coefficients for internal energy for spin-1/2 Ising model on f.c.c. lattice.

6, 24, 132, 816, 5448, 38808, 290568, 2255232, 17981532, 146428728, 1213014960, 10192820592, 86687830596, 744919762584

Offset

1,1

Links

Table of n, a(n) for n=1..14.

M. E. Fisher and M. F. Sykes, Antiferromagnetic susceptibilities of the simple cubic and body-centered cubic Ising lattices, Physica, 28 (1962), 939-956.

S. McKenzie, Extended high-temperature series expansions for the spin-s Ising model, J. Phys. A: Math. Gen., 16 (1983), 2875-2880. See table 1, column c(n); divide by 2 to get a(n).

M. F. Sykes, J. L. Martin and D. L. Hunter, Specific heat of a three-dimensional Ising ferromagnet above the Curie temperature, Proc. Phys. Soc., 91 (1967), 671-677.

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

Formula

G.f. 6*v + 24*v^2 + 132*v^3 + 816*v^4 ... = v*q/2 + (1-v^2) * f'(v) / f(v), where f(v) = 1 + 8*v^3 + 33*v^4 + ... is the g.f. of A001407 and q = 12 is the number of nearest neighbors. - Andrey Zabolotskiy, Feb 14 2022

Crossrefs

Cf. A010571 (cubic), A047711 (b.c.c.), A001407 (partition function), A002918 (specific heat).

Sequence in context: A052170 A027224 A110707 * A188330 A126267 A026947

Adjacent sequences: A047709 A047710 A047711 * A047713 A047714 A047715

Keyword

nonn,more

Author

N. J. A. Sloane

Extensions

a(9)-a(11) from Sykes, Martin & Hunter added by Andrey Zabolotskiy, Feb 05 2022

Name clarified and a(12)-a(13) added by Andrey Zabolotskiy, Feb 14 2022

a(14) from McKenzie added by Andrey Zabolotskiy, Jan 18 2023

Status

approved