A001393 High temperature series for spin-1/2 Ising free energy on 3-dimensional simple cubic lattice.

1, 0, 3, 22, 192, 2046, 24853, 329334, 4649601, 68884356, 1059830112, 16809862992, 273374177222, 4539862959852, 76744615270821, 1317316023432372, 22913901542478978, 403242080061821802, 7169757254509112094, 128654570700129670404, 2327634530912450464791, 42424918919225263486322, 778469235834728913157632, 14371906938404203811137770

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• nice

Comments

z = exp(-f/T) = 2 * cosh(K)^3 * Sum_{n >= 0} a(n) * v^(2*n) where v = tanh(K), K = J/T, T is temperature (in the units of energy), J is the nearest-neighbor interaction, and f is the free energy per spin. See Wipf, pp. 181-182. z is the [geometric average] partition function per spin, so the original name of this entry, "Partition function for cubic lattice", is somewhat more directly related to this sequence. - Andrey Zabolotskiy, Oct 18 2021

References

• S. R. Finch, Mathematical Constants, Cambridge, 2003, pp. 391-406.
• 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).
• Andreas Wipf, Statistical Approach to Quantum Field Theory, LNP 864, Springer, 2013.

Links

• Steven R. Finch, Lenz-Ising Constants [broken link]
• Steven R. Finch, Lenz-Ising Constants [From the Wayback Machine]
• A. J. Guttmann and I. G. Enting, Series studies of the Potts model: I. The simple cubic Ising model, J. Phys. A 26 (1993) 807-821; arXiv:hep-lat/9212032.
• A. J. Guttmann and I. G. Enting, The high-temperature specific heat exponent of the 3-dimensional Ising model, J. Phys. A 27 (1994) 8007-8010; arXiv:cond-mat/9411002.
• G. S. Rushbrooke and J. Eve, High-temperature Ising partition function and related noncrossing polygons for the simple cubic lattice, J. Math. Physics 3 (1962) 185-189. Gives correct a(0)-a(6) and incorrect a(7).
• Index entries for sequences related to specific heat

Crossrefs

Cf. A001406, A001407, A002891, A010571.

Extensions

Corrections and updates from Steven Finch

a(14)-a(23) from Andrey Zabolotskiy, Oct 18 2021