cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A002928 Magnetization for square lattice.

Original entry on oeis.org

1, 0, -2, -8, -34, -152, -714, -3472, -17318, -88048, -454378, -2373048, -12515634, -66551016, -356345666, -1919453984, -10392792766, -56527200992, -308691183938, -1691769619240, -9301374102034
Offset: 0

Views

Author

N. J. A. Sloane, Simon Plouffe

Keywords

References

  • 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).
  • J. M. Yeomans, Statistical mechanics of phase transitions, Oxford Univ. Press, 1992, p. 93.

Links

Crossrefs

Cf. other structures: A007206, A007207, A002929, A002930, A003193, A003196.
Cf. higher spins: A010102, A010105/A030120, A010103, A010106/A030121, A010104.
Cf. Potts model: A057374, A057378.
Cf. A002927 (susceptibility).

Programs

  • Maple
    series((1+x)^(1/4)*(1-6*x+x^2)^(1/8)/(1-x)^(1/2),x,40).
  • Mathematica
    CoefficientList[Series[(1+x)^(1/4)*(1-6*x+x^2)^(1/8)/(1-x)^(1/2), {x, 0, 20}], x] (* Vaclav Kotesovec, Apr 27 2024 *)

Formula

n*a(n) + 6*(-n+1)*a(n-1) + 4*a(n-2) + 6*(n-3)*a(n-3) + (-n+4)*a(n-4) = 0. - R. J. Mathar, Mar 08 2013
a(n) ~ -Gamma(1/8) * (1 + sqrt(2))^(2*n - 1/2) / (Pi * 2^(57/16) * n^(9/8)). - Vaclav Kotesovec, Apr 27 2024

A002914 Susceptibility series for b.c.c. lattice.

Original entry on oeis.org

1, 8, 56, 392, 2648, 17864, 118760, 789032, 5201048, 34268104, 224679864, 1472595144, 9619740648, 62823141192, 409297617672, 2665987056200, 17333875251192, 112680746646856, 731466943653464, 4747546469665832, 30779106675700312, 199518218638233896, 1292141318087690824, 8367300424426139624, 54141252229349325768, 350288350314921653160
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

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.
  • 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

Extensions

More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Mar 01 2008
a(24)-a(25) from Campostrini added by Andrey Zabolotskiy, Feb 09 2022

A002921 Susceptibility series for f.c.c. lattice.

Original entry on oeis.org

1, 12, 132, 1404, 14652, 151116, 1546332, 15734460, 159425580, 1609987708, 16215457188, 162961837500, 1634743178420, 16373484437340, 163778159931180, 1636328839130860
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

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.
  • 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

Crossrefs

Cf. A002913 (cubic), A002914 (b.c.c.); A002918 (specific heat).
Cf. Heisenberg model: A002166; A002170 (cubic), A002168 (b.c.c.); A002165 (specific heat).

Extensions

a(13)-a(15) from McKenzie added by Andrey Zabolotskiy, Feb 05 2022

A002929 Magnetization for cubic lattice.

Original entry on oeis.org

1, 0, 0, -2, 0, -12, 14, -90, 192, -792, 2148, -7716, 23262, -79512, 252054, -846628, 2753520, -9205800, 30371124, -101585544, 338095596, -1133491188, 3794908752, -12758932158, 42903505030, -144655483440, 488092130664, -1650000819068, 5583090702798, -18918470423736, 64167341172984, -217893807812346, 740578734923544
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

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.
  • 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).
  • Andreas Wipf, Statistical Approach to Quantum Field Theory, LNP 864, Springer, 2013. See Table 9.6, beware of the typo in a(12).

Links

Extensions

a(21)-a(32) from Wipf added by Andrey Zabolotskiy, Oct 18 2021

A003196 Magnetization series for face-centered cubic lattice.

Original entry on oeis.org

1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -24, 26, 0, 0, -48, -252, 720, -438, -192, -984, -1008, 12924, -19536, 3062, -8280, 26694, 153536, -507948, 406056, -79532, 729912, 631608, -9279376, 15771600, -7467336, 10935114, -21835524, -112752684, 400576168, -410287368
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

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. [has a typo in a(35)]
  • N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Crossrefs

Cf. A003193.

A007216 Low temperature antiferromagnetic susceptibility for diamond.

Original entry on oeis.org

1, 0, 4, 0, 16, 24, 122, 348, 1266, 4464, 16394, 57932, 215916, 828348
Offset: 0

Views

Author

Simon Plouffe

Keywords

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

Links

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

Crossrefs

Cf. A003195.

A002912 Low-temperature series in z = exp(-2J/kT) for ferromagnetic susceptibility for the Ising model on honeycomb structure.

Original entry on oeis.org

0, 0, 1, 6, 27, 122, 516, 2148, 8792, 35622, 143079, 570830, 2264649, 8942436, 35169616, 137839308, 538594704, 2098892928, 8159937669, 31656305550, 122575164923, 473797120338, 1828512928200, 7046581314292, 27119735418924, 104247226432566, 400272672674603
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

Comments

Previous name was: Susceptibility coefficients for honeycomb.

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.
  • 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

Crossrefs

Cf. A002978.

Extensions

New name and more terms from Chan et al added by Andrey Zabolotskiy, Mar 03 2021

A002930 Magnetization series for diamond.

Original entry on oeis.org

1, 0, -2, -8, -26, -80, -268, -944, -3474, -13072, -49672, -191272, -744500, -2924680, -11596284, -46364456
Offset: 0

Views

Author

N. J. A. Sloane, Simon Plouffe

Keywords

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

Links

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

A003193 Magnetization for body-centered cubic lattice.

Original entry on oeis.org

1, 0, 0, 0, -2, 0, 0, -16, 18, 0, -168, 384, -314, -1632, 6264, -9744, -10014, 86976, -205344, 80176, 1009338, -3579568, 4575296, 8301024, -54012882, 112640896, -5164464, -694845120, 2160781086
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

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

Links

Crossrefs

Cf. A002929 (cubic), A003196 (f.c.c.), A002925 (ferromagnetic susceptibility), A003194 (antiferromagnetic susceptibility).

Extensions

a(27)-a(28) from Sykes et al. (1973) added by Andrey Zabolotskiy, Feb 16 2022

A007218 Low temperature series for spin-1/2 Ising antiferromagnetic susceptibility for 3-dimensional b.c.c. lattice.

Original entry on oeis.org

1, 0, 0, 0, -2, 0, 28, -64, 39, 224, -884, 1368, 1350, -12272, 28752, -11944, -138873, 494184, -640856, -1111568, 7363194, -15488224, 1198848, 93506112, -293473869
Offset: 0

Views

Author

N. J. A. Sloane, Simon Plouffe

Keywords

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

Links

Crossrefs

Cf. A003194.

Formula

a(n) = A003194(n+4)/4. - Andrey Zabolotskiy, Feb 16 2022

Extensions

Corrections and updates from Steven Finch
Previous Showing 11-20 of 28 results. Next

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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