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A001393
High temperature series for spin-1/2 Ising free energy on 3-dimensional simple cubic lattice.
(Formerly M3093 N1253)
9
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
0,3
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).
CROSSREFS
KEYWORD
nonn,nice
EXTENSIONS
Corrections and updates from Steven Finch
a(14)-a(23) from Andrey Zabolotskiy, Oct 18 2021
STATUS
approved