A002915 -id:A002915 - cp's OEIS frontend

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

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

N. J. A. Sloane

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).

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.

Cf. other quantities: A001393 (partition function), A010571 (internal energy), A002916 (specific heat), A003490 (surface susceptibility), A007287 (layer susceptibility), A010040, A010043, A010046.
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).

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

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

Original entry on oeis.org

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

N. J. A. Sloane

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.

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.

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.).

Corrections and updates from Steven Finch

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

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

Original entry on oeis.org

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

N. J. A. Sloane, C. Vohwinkel

sign

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).

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.

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

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)

A002979 Low-temperature series in exp(4J/kT) for antiferromagnetic susceptibility for the Ising model on square lattice.

Original entry on oeis.org

0, 4, 0, 16, 32, 156, 608, 2688, 12064, 55956, 266656

Offset: 1

N. J. A. Sloane

Previous name was: Susceptibility series for square lattice.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

M. F. Sykes, D. G. Gaunt, P. D. Roberts and J. A. Wyles, High temperature series for the susceptibility of the Ising model, I. Two dimensional lattices, J. Phys. A 5 (1972) 624-639.

Cf. A007215, A002915 (cubic), A002978 (honeycomb), A002927 (ferromagnetic).

a(n) = 4*A007215(n-2). - Andrey Zabolotskiy, Mar 03 2021

New name from Andrey Zabolotskiy, Mar 03 2021

cp's OEIS Frontend

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

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

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

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A002979 Low-temperature series in exp(4J/kT) for antiferromagnetic susceptibility for the Ising model on square lattice.

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