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%I M3093 N1253 #35 Feb 14 2022 07:33:15
%S 1,0,3,22,192,2046,24853,329334,4649601,68884356,1059830112,
%T 16809862992,273374177222,4539862959852,76744615270821,
%U 1317316023432372,22913901542478978,403242080061821802,7169757254509112094,128654570700129670404,2327634530912450464791,42424918919225263486322,778469235834728913157632,14371906938404203811137770
%N High temperature series for spin-1/2 Ising free energy on 3-dimensional simple cubic lattice.
%C 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
%D S. R. Finch, Mathematical Constants, Cambridge, 2003, pp. 391-406.
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%D Andreas Wipf, Statistical Approach to Quantum Field Theory, LNP 864, Springer, 2013.
%H Steven R. Finch, <a href="http://www.people.fas.harvard.edu/~sfinch/constant/ising/ising.html">Lenz-Ising Constants</a> [broken link]
%H Steven R. Finch, <a href="http://web.archive.org/web/20010207201511/http://www.mathsoft.com:80/asolve/constant/ising/ising.html">Lenz-Ising Constants</a> [From the Wayback Machine]
%H A. J. Guttmann and I. G. Enting, <a href="https://doi.org/10.1088/0305-4470/26/4/010">Series studies of the Potts model: I. The simple cubic Ising model</a>, J. Phys. A 26 (1993) 807-821; arXiv:<a href="https://arxiv.org/abs/hep-lat/9212032">hep-lat/9212032</a>.
%H A. J. Guttmann and I. G. Enting, <a href="https://doi.org/10.1088/0305-4470/27/24/012">The high-temperature specific heat exponent of the 3-dimensional Ising model</a>, J. Phys. A 27 (1994) 8007-8010; arXiv:<a href="https://arxiv.org/abs/cond-mat/9411002">cond-mat/9411002</a>.
%H G. S. Rushbrooke and J. Eve, <a href="https://doi.org/10.1063/1.1703777">High-temperature Ising partition function and related noncrossing polygons for the simple cubic lattice</a>, J. Math. Physics 3 (1962) 185-189. Gives correct a(0)-a(6) and incorrect a(7).
%H <a href="/index/Sp#specific_heat">Index entries for sequences related to specific heat</a>
%Y Cf. A001406, A001407, A002891, A010571.
%K nonn,nice
%O 0,3
%A _N. J. A. Sloane_
%E Corrections and updates from _Steven Finch_
%E a(14)-a(23) from _Andrey Zabolotskiy_, Oct 18 2021
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