A002926 Low temperature series for spin-1/2 Ising magnetic susceptibility on 3-dimensional simple cubic lattice. (Formerly M4823 N2064)

0, 0, 1, 0, 12, -14, 135, -276, 1520, -4056, 17778, -54392, 213522, -700362, 2601674, -8836812, 31925046, -110323056, 393008712, -1369533048, 4844047090, -16947396000, 59723296431, -209328634116, 736260986208, -2582605180212, 9074182912884

Offset

1,5

References

C. Domb, Ising model, in Phase Transitions and Critical Phenomena, vol. 3, ed. C. Domb and M. S. Green, Academic Press, 1974; p. 421.

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).

C. Vohwinkel, personal communication.

Links

Andrei Zabolotskii, Table of n, a(n) for n = 1..32

Gyan Bhanot, Michael Creutz, Ivan Horvath, Jan Lacki and John Weckel, Series expansions without diagrams, Phys. Rev. E, 49 (1994), 2445-2453; arXiv:hep-lat/9303002, 1993.

C. Domb, Ising model, Phase Transitions and Critical Phenomena 3 (1974), 257, 380-381, 384-387, 390-391, 412-423. (Annotated scanned copy)

J. W. Essam and M. E. Fisher, Padé approximant studies of the lattice gas and Ising ferromagnet below the critical point, J. Chem. Phys., 38 (1963), 802-812.

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.

Elmar Siepmann, Reihenanalysen für das 3-dimensionale Ising-Modell, Westfälische Wilhelms-Universität Münster, 1993. See Eq. (A.13); divide the coefficients by 4 to get this sequence.

M. F. Sykes et al., Derivation of low-temperature expansions for Ising model VI. Three-dimensional lattices - temperature grouping, J. Phys. A 6 (1973), 1507-1516.

Crossrefs

Cf. A002913 (high temperature series); other quantities: A002915 (antiferromagnetic susceptibility), A002891 (partition function), A002929 (magnetization); other lattices: A002927 (square), A002924 (f.c.c.), A002925 (b.c.c.).

Sequence in context: A058073 A058951 A287916 * A318298 A139310 A221819

Adjacent sequences: A002923 A002924 A002925 * A002927 A002928 A002929

Keyword

sign,nice

Author

N. J. A. Sloane

Extensions

Corrections and updates from Steven Finch

a(25)-a(27) from Bhanot et al. added by Andrei Zabolotskii, Feb 09 2022

Status

approved