A002892 -id:A002892 - cp's OEIS frontend

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

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

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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)

A001407 High temperature series for partition function for spin-1/2 Ising model on f.c.c. lattice.

Original entry on oeis.org

1, 0, 0, 8, 33, 168, 962, 5928, 38907, 268056, 1918938, 14169360, 107333498, 830660688, 6546655404, 52410001448

Offset: 0

N. J. A. Sloane

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. Domb and M. F. Sykes, The calculation of lattice constants in crystal statistics, Phil. Mag., 2 (1957), 733ff.
M. F. Sykes, D. L. Hunter, D. S. McKenzie and B. R. Heap, Specific heat of a three dimensional Ising ferromagnet above the Curie temperature. II, J. Phys. A: Gen. Phys., 5 (1972), 667-673. The power-series part of Eq. (1.3) is the logarithm of the g.f. for this sequence.
Index entries for sequences related to f.c.c. lattice

Cf. A001393, A001406, A002892, A047712, A002918.

a(10)-a(14) added and name clarified by Andrey Zabolotskiy, Feb 14 2022

a(15) added using data from A047712 by Andrey Zabolotskiy, Jan 18 2023

A002924 Ferromagnetic susceptibility series for f.c.c. lattice.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 24, -26, 0, 0, 72, 378, -1080, 665, 384, 1968, 2016, -25698, 39552, -3872, 20880, -65727, -379072, 1277646, -986856, 176978, -2163504, -1818996, 27871080, -47138844, 20789424, -36509652, 77055330, 393046656, -1402934816, 1403843388

Offset: 0

N. J. A. Sloane

sign

C. Domb, Ising model, in Phase Transitions and Critical Phenomena, vol. 3, ed. C. Domb and M. S. Green, Academic Press, 1974; p. 421.
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. 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.
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.
Index entries for sequences related to f.c.c. lattice

Cf. A002926 (cubic), A002925 (b.c.c.), A002892 (partition function), A003196 (magnetization), A002921 (high-temperature).

a(35)-a(40) from Sykes et al. added by Andrey Zabolotskiy, Feb 16 2022

A371049 Low temperature series for spin-1/2 Ising partition function on body-centered cubic lattice.

Original entry on oeis.org

1, 0, 0, 0, 1, 0, 0, 4, -4, 0, 28, -60, 44, 204, -750, 1084, 979, -8444, 18886, -7568, -82269, 280288, -348172, -576712, 3677331, -7445964, 569558, 41740944, -126624684

Offset: 1

Andrey Zabolotskiy, Mar 11 2024

The series is in the variable u = exp(-4J/kT).

The expansion of the logarithm of the g.f. of this sequence is given in Domb & Guttmann's Table 1 (with a reference to Sykes et al., 1965) and continued in Eq. (4.14) of Sykes et al., 1973.

Claude Itzykson and Jean-Michel Drouffe, Statistical field theory, vol. 2, Cambridge University Press, 1989. Eq. (120) is supposed to give the logarithm of the g.f., but its second half is erroneously switched with the second half of Eq. (121). These second halves are Eqs. (4.15) and (4.14) of Sykes et al., 1973.

C. Domb and A. J. Guttmann, Low-temperature series for the Ising model, J. Phys. C: Solid State Phys., 3 (1970), 1652-1660.
M. F. Sykes, J. W. Essam and D. S. Gaunt, Derivation of low-temperature expansions for the Ising model of a ferromagnet and an antiferromagnet, J. Math. Phys. 6 (1965), 283-298.
M. F. Sykes, D. S. Gaunt, J. W. Essam and C. J. Elliott, Derivation of low-temperature expansions for Ising model. VI. Three-dimensional lattices-temperature grouping, J. Phys. A: Math. Nucl. Gen., 6 (1973), 1507-1516.
Index entries for sequences related to b.c.c. lattice

Cf. A002891 (simple cubic), A002892 (f.c.c.); A003193 (magnetization), A002925 (ferromagnetic susceptibility), A007218 (antiferromagnetic susceptibility); A001406 (high temperature).

cp's OEIS Frontend

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

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A001407 High temperature series for partition function for spin-1/2 Ising model on f.c.c. lattice.

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A002924 Ferromagnetic susceptibility series for f.c.c. lattice.

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A371049 Low temperature series for spin-1/2 Ising partition function on body-centered cubic lattice.

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