A010571 High temperature expansion of -u/J in odd powers of v = tanh(J/kT), where u is energy per site of the spin-1/2 Ising model on cubic lattice with nearest-neighbor interaction J at temperature T.

3, 12, 120, 1368, 18300, 268728, 4179852, 67767744, 1133826324, 19443072084, 340085761968, 6046276240668, 108970501777080, 1986820814551056, 36587507853481908, 679619087721892176, 12720247240214281860, 239685390231729125004, 4543441582487318876664

Offset

1,1

Links

Table of n, a(n) for n=1..19.

M. E. Fisher and D. S. Gaunt, Ising model and self-avoiding walks on hypercubical lattices and high density expansions, Phys. Rev., 133 (1964), A224-A239. See Table II for correct a(1)-a(6) but incorrect a(7).

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

Formula

Sum_{n>=1} a(n) * v^(2*n-1) = v*q/2 + (1-v^2) * f'(v) / f(v), where f(v) = Sum_{n>=0} A001393(n) * v^(2*n) and q = 6 is the number of nearest neighbors. - Andrey Zabolotskiy, Feb 14 2022

Crossrefs

Cf. A001393, A002908, A007239, A010572-A010574, A047711, A047712.

Sequence in context: A280458 A294198 A133553 * A280248 A067124 A208937

Adjacent sequences: A010568 A010569 A010570 * A010572 A010573 A010574

Keyword

nonn,nice

Author

N. J. A. Sloane

Extensions

New name from Andrey Zabolotskiy, Jan 14 2019

a(7) corrected and more terms added by Andrey Zabolotskiy, Feb 14 2022

Status

approved