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
Links
- 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
Extensions
New name from Andrey Zabolotskiy, Jan 14 2019
a(7) corrected and more terms added by Andrey Zabolotskiy, Feb 14 2022