A002891 Low temperature series for spin-1/2 Ising partition function on 3-dimensional simple cubic lattice. (Formerly M2293 N0906)

1, 0, 0, 1, 0, 3, -3, 15, -30, 101, -261, 807, -2308, 7065, -21171, 65337, -200934, 627249, -1962034, 6192066, -19610346, 62482527, -199807110, 641837193, -2068695927, 6691611633, -21710041944, 70645706963, -230488840446, 753903842400, -2471624380458, 8120879664294, -26736570257010

Offset

0,6

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).

Links

Table of n, a(n) for n=0..32.

Daniel Andrén, Series expansion for the density of states of the Ising and Potts models, arXiv:0706.3116 [cond-mat.str-el], 2007.

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, 1992.

A. J. Wakefield, Statistics of the simple cubic lattice, Proc. Cambridge Philos. Soc. 47 (1951) 419-435 and 799-810.

Crossrefs

Cf. A002926 (ferromagnetic susceptibility), A002915 (antiferromagnetic susceptibility), A001393 (high-temperature), A002890 (square lattice), A002892 (f.c.c. lattice), A030045 (4D cubic), A030047 (5D cubic).

Sequence in context: A153512 A369358 A127328 * A089875 A035617 A126319

Adjacent sequences: A002888 A002889 A002890 * A002892 A002893 A002894

Keyword

sign

Author

N. J. A. Sloane, C. Vohwinkel

Extensions

Corrections and updates from Steven Finch

"Free energy" changed back to "partition function" (basically the exponential of the free energy) in the name by Andrey Zabolotskiy, Feb 12 2022

a(28)-a(32) added by Andrey Zabolotskiy, Jun 30 2022 using Andrén's data (see his Table 2, column a_n for the coefficients of the expansion of the logarithm of the g.f. of this sequence)

Status

approved