A001393 High temperature series for spin-1/2 Ising free energy on 3-dimensional simple cubic lattice. (Formerly M3093 N1253)

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

Table of n, a(n) for n=0..23.

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.

Sequence in context: A278333 A132595 A065204 * A046743 A121952 A367393

Adjacent sequences: A001390 A001391 A001392 * A001394 A001395 A001396

Keyword

nonn,nice

Author

N. J. A. Sloane

Extensions

Corrections and updates from Steven Finch

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

Status

approved