A010047 -id:A010047 - cp's OEIS frontend

A010556 High temperature series for spin-1/2 Ising magnetic susceptibility on 4D simple cubic lattice.

1, 8, 56, 392, 2696, 18536, 126536, 863720, 5873768, 39942184, 271009112, 1838725896, 12457092504, 84392312392, 571140732808, 3865210690888, 26138072412040, 176752645426600, 1194553221342296, 8073068110703880, 54534614510976680

Offset: 0

N. J. A. Sloane

nonn

S. R. Finch, Mathematical Constants, Cambridge, 2003, pp. 391-406.

P. Butera and M. Pernici, High-temperature expansions of the higher susceptibilities for the Ising model in general dimension d, Phys. Rev. E 86, 011139 (2012); arXiv:1209.3592 [hep-lat], 2012.
Steven R. Finch, Lenz-Ising Constants [broken link]
Steven R. Finch, Lenz-Ising Constants [From the Wayback Machine]
M. E. Fisher and D. S. Gaunt, Ising model and self-avoiding walks on hypercubical lattices and high density expansions, Phys. Rev. 133 (1964), A224-A239.
D. S. Gaunt, M. F. Sykes and S. McKenzie, Susceptibility and fourth-field derivative of the spin-1/2 Ising model for T > T_c and d = 4, J. Phys. A 12 (1979), 871-877.
M. A. Moore, Critical behavior of the four-dimensional Ising ferromagnet and the breakdown of scaling, Phys. Rev. B 1 (1970), 2238-2240.

Cf. A002906 (2D), A002913 (3D), A010579 (5D), A010580 (6D), A030008 (7D).

Cf. A030046, A010041, A010044, A010047.

a(17) corrected (was 176752645540264), a(18)-a(20) added using Butera & Pernici's formulas by Andrey Zabolotskiy, Aug 08 2022

A010046 High-temperature expansion of Ising model susceptibility chi_4 for cubic lattice.

Original entry on oeis.org

2, 48, 1272, 38784, 1341408, 52186368, 2256454272, 107494477824, 5595152936448, 316081923944448, 19262189406185472, 1259828274265227264, 88026828815690047488, 6544693787367160086528, 515907116666737635459072, 42981965201161894878511104, 3773829205951827807017238528

Offset: 0

N. J. A. Sloane

nonn

P. Butera and M. Pernici, High-temperature expansions of the higher susceptibilities for the Ising model in general dimension d, Phys. Rev. E 86, 011139 (2012); arXiv:1209.3592 [hep-lat], 2012. Appendix A gives chi_4 as a function of K, which is the negated e.g.f. of this sequence at d=3.
M. Lüscher and P. Weisz, Application of the linked cluster expansion to the n-component phi^4 theory, Nuclear Physics B 300 (1988), 325-359.

Cf. A010045 (square), A010047 (4D cubic), A010040 (chi_2, see also A002913), A010043 (mu_2).

Name clarified, a(14)-a(16) using Butera & Pernici's formulas added by Andrey Zabolotskiy, Nov 25 2024

A010041 High-temperature expansion of Ising model susceptibility chi_2 for 4-d cubic lattice.

Original entry on oeis.org

1, 8, 112, 2336, 63808, 2177408, 88532992, 4198893056, 226756461568, 13774782507008, 927722457014272, 68724458864869376, 5545864378385072128, 484804579241630302208, 45594217495265300119552, 4594089494167496649015296, 493393425754870454072639488, 56299361591526976658442027008

Offset: 0

N. J. A. Sloane

nonn

M. Lüscher and P. Weisz, Application of the linked cluster expansion to the n-component phi^4 theory, Nuclear Physics B 300 (1988), 325-359.

Cf. A010556, A010039 (square), A010040 (cubic), A010044 (mu_2), A010047 (chi_4).

E.g.f.: F(tanh(x)), where F(x) is the g.f. of A010556. - Andrey Zabolotskiy, Nov 19 2024

Name clarified, terms a(15)-a(17) using data from A010556 added by Andrey Zabolotskiy, Nov 25 2024

A010045 High-temperature expansion of Ising model susceptibility chi_4 for square lattice.

Original entry on oeis.org

2, 32, 528, 9728, 197568, 4424192, 108461568, 2895515648, 83657776128, 2602257293312, 86733041246208, 3084465770528768, 116595295651135488, 4668952802696364032, 197452751427562242048, 8794599595709419225088, 411518238008892605595648, 20183379315419545025380352

Offset: 0

N. J. A. Sloane

nonn

P. Butera and M. Pernici, High-temperature expansions of the higher susceptibilities for the Ising model in general dimension d, Phys. Rev. E 86, 011139 (2012); arXiv:1209.3592 [hep-lat], 2012. Appendix A gives chi_4 as a function of K, which is the negated e.g.f. of this sequence at d=2.
M. Lüscher and P. Weisz, Application of the linked cluster expansion to the n-component phi^4 theory, Nuclear Physics B 300 (1988), 325-359.

Cf. A010046 (cubic), A010047 (4D cubic), A010039 (chi_2, see also A002906), A010042 (mu_2).

Name clarified, a(15)-a(17) using Butera & Pernici's formulas added by Andrey Zabolotskiy, Nov 25 2024

A010557 Fourth-field derivative of Ising model free energy for 4-d cubic lattice.

Original entry on oeis.org

1, 32, 584, 8288, 101240, 1121120, 11570360, 113293088, 1064631032, 9681082144, 85688330696, 741562925664, 6296196525768, 52589092312288, 433044168426616, 3521747918221984, 28326976016327032, 225625290109912096, 1781402824552864712, 13954143265951219296, 108525895871787179576

Offset: 0

N. J. A. Sloane

nonn

P. Butera and M. Pernici, High-temperature expansions of the higher susceptibilities for the Ising model in general dimension d, Phys. Rev. E 86, 011139 (2012); arXiv:1209.3592 [hep-lat], 2012.
D. S. Gaunt, M. F. Sykes and S. McKenzie, Susceptibility and fourth-field derivative of the spin-1/2 Ising model for T > T_c and d = 4, J. Phys. A 12 (1979), 871-877.

Cf. A010047, A010556, A010572.

Name clarified, a(17)-a(20) using Butera & Pernici's formulas added by Andrey Zabolotskiy, Nov 25 2024

A010367 High-temperature spin-1/2 Ising model series for second derivative of susceptibility with respect to magnetic field for hyper-body-centered-cubic lattice.

Original entry on oeis.org

2, 128, 9792, 886784, 92722944, 11014965248, 1465369976832, 215937597784064, 34916329300783104, 6147843514432913408, 1170908043876450435072

Offset: 1

N. J. A. Sloane

Moore defines two four-dimensional lattices called hbcc ("hyper-body-centered-cubic") and hfcc. They have essentially the same arrangement of sites, up to a similarity transformation. (That set of sites forms the D_4 lattice.) However the sets of bonds are different: each site of hfcc is connected to all 24 of its nearest neighbors, while each site of hbcc is connected only to 16 of them, specifically those which have relative position vector (+-1, +-1, +-1, +-1), but not (+-2, 0, 0, 0) or its permutations. - Andrey Zabolotskiy, Nov 26 2024

George A. Baker Jr. and John M. Kincaid, The continuous-spin Ising model, g0:phi4:d field theory and the renormalization group. J. Statist. Phys. 24 (1981), no. 3, 469-528. See Eq. (4.27).
M. A. Moore, Critical Behavior of the Four-Dimensional Ising Ferromagnet and the Breakdown of Scaling, Phys. Rev. B 1, 2238-2240 (1970).
Index entries for sequences related to D_4 lattice

Cf. A010047, A010559, A010560, A010564.

Edited by Andrey Zabolotskiy, Aug 01 2022 and Nov 26 2024

cp's OEIS Frontend

A010556 High temperature series for spin-1/2 Ising magnetic susceptibility on 4D simple cubic lattice.

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A010046 High-temperature expansion of Ising model susceptibility chi_4 for cubic lattice.

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A010041 High-temperature expansion of Ising model susceptibility chi_2 for 4-d cubic lattice.

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A010045 High-temperature expansion of Ising model susceptibility chi_4 for square lattice.

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A010557 Fourth-field derivative of Ising model free energy for 4-d cubic lattice.

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A010367 High-temperature spin-1/2 Ising model series for second derivative of susceptibility with respect to magnetic field for hyper-body-centered-cubic lattice.

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