A002913 High temperature series for spin-1/2 Ising magnetic susceptibility on 3-dimensional simple cubic lattice. (Formerly M4201 N1753)

1, 6, 30, 150, 726, 3510, 16710, 79494, 375174, 1769686, 8306862, 38975286, 182265822, 852063558, 3973784886, 18527532310, 86228667894, 401225368086, 1864308847838, 8660961643254, 40190947325670, 186475398518726, 864404776466406, 4006394107568934, 18554916271112254, 85923704942057238

Offset

0,2

References

C. Domb, Ising model, in Phase Transitions and Critical Phenomena, vol. 3, ed. C. Domb and M. S. Green, Academic Press, 1974; p. 381.

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

Andrey Zabolotskiy, Table of n, a(n) for n = 0..32 (terms a(24), a(25) taken from the Campostrini et al. 2002 article by Per H. Lundow, terms a(26)-a(32) taken from the Toshiaki Fujiwara and Hiroaki Arisue's slides)

P. Butera and M. Comi, N-vector spin models on the simple-cubic and the body-centered-cubic lattices: A study of the critical behavior of the susceptibility and of the correlation length by high-temperature series extended to order beta^21, Phys. Rev. B 56 (1997) 8212-8240; arXiv:hep-lat/9703018, 1997.

P. Butera and M. Comi, Extension to order b23 of the high-temperature expansions for the spin-1/2 Ising model on the simple-cubic and the body-centered-cubic lattices, BICOCCA/FT-00-09 (June 2000). Phys. Rev. B62 (2000) 14837-14843.

M. Campostrini, Linked-Cluster Expansion of the Ising Model, Journal of Statistical Physics, 103 (2001), 369-394.

M. Campostrini, A. Pelissetto, P. Rossi, and E. Vicari, 25th-order high-temperature expansion results for three-dimensional Ising-like systems on the simple-cubic lattice, Phys. Rev. E, 65 (2002), 66-127.

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

Steven R. Finch, Lenz-Ising Constants [broken link]

Steven R. Finch, Lenz-Ising Constants [From the Wayback Machine]

M. E. Fisher and R. J. Burford, Theory of critical point scattering and correlations I: the Ising model, Phys. Rev. 156 (1967), 583-621.

Toshiaki Fujiwara and Hiroaki Arisue (presenter), ３次元イジング模型の高温展開 (High-temperature expansion for the 3D Ising model), Computational Physics with CP-PACS 2002 Workshop [in Japanese].

Toshiaki Fujiwara and Hiroaki Arisue (presenter), New algorithm of the high-temperature expansion for the Ising model in three dimensions, Asia-Pacific Mini-Workshop on Lattice QCD, Center for Computational Physics, University of Tsukuba, 2003: abstract, slides, source.

D. S. Gaunt, High Temperature Series Analysis for the Three-Dimensional Ising Model: A Review of Some Recent Work, pp. 217-246 in: Phase Transitions: Cargèse 1980, eds. Maurice Lévy, Jean-Claude Le Guillou and Jean Zinn-Justin, Springer, Boston, MA, 1982.

M. F. Sykes, D. G. Gaunt, P. D. Roberts and J. A. Wyles, High temperature series for the susceptibility of the Ising model, II. Three dimensional lattices, J. Phys. A 5 (1972) 640-652.

Crossrefs

Cf. other quantities: A001393 (partition function), A010571 (internal energy), A002916 (specific heat), A003490 (surface susceptibility), A007287 (layer susceptibility).

Cf. other structures: A002906 (square), A002920 (hexagonal), A002910 (honeycomb), A002914 (b.c.c.), A002921 (f.c.c.), A003119 (diamond), A010556 (4D cubic), A010579 (5D cubic), A010580 (6D cubic), A030008 (7D cubic).

Cf. low-temperature series: A002926 (ferromagnetic), A002915 (antiferromagnetic).

Cf. other models: A002170 (Heisenberg), A003279 (spherical), A010040, A010043, A010046 (phi^4 theory).

Sequence in context: A127741 A073965 A214940 * A157519 A075886 A001412

Adjacent sequences: A002910 A002911 A002912 * A002914 A002915 A002916

Keyword

nonn,nice

Author

N. J. A. Sloane

Extensions

Corrections and updates from Steven Finch

More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Mar 01 2008

Several errors in the sequence were corrected by Per H. Lundow, Jan 17 2011

Status

approved