A010045 -id:A010045 - cp's OEIS frontend

A010047 High-temperature expansion of Ising model susceptibility chi_4 for 4-d cubic lattice.

2, 64, 2336, 99328, 4840832, 267080704, 16467255296, 1123220758528, 83995566282752, 6835730843582464, 601493660302278656, 56912420061511548928, 5762378580637148905472, 621705383408527748890624, 71206666963479522492809216

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. A010557, A010041 (chi_2), A010044 (mu_2), A010045 (square), A010046 (cubic).

E.g.f.: 2*F(tanh(x)), where F(x) is the g.f. of A010557. - Andrey Zabolotskiy, Nov 19 2024

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

A010039 High-temperature expansion of Ising model susceptibility chi_2 for square lattice.

Original entry on oeis.org

1, 4, 24, 208, 2208, 28864, 440064, 7752448, 153604608, 3398247424, 82812002304, 2208100261888, 63835179614208, 1991789102301184, 66630050985836544, 2381273427126550528, 90474637735806763008, 3643995535114567942144, 154996077159081295478784, 6946094284451252292026368

Offset: 0

N. J. A. Sloane

nonn

It appears that a(n) is divisible by 2^n, and a(2n) is additionally divisible by 3. - Ralf Stephan, Aug 04 2013

Laurent Pierre, Bernard Bernu and Laura Messio, High temperature series expansions of S = 1/2 Heisenberg spin models: Algorithm to include the magnetic field with optimized complexity, SciPost Phys. 17, 105 (2024); arXiv:2404.02271 [cond-mat.str-el], 2024. See the supporting file SquareIsing_18_1.py; multiply pol1[1] by 2 to get this sequence.
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. A002906, A010040 (cubic), A010042 (mu_2), A010045 (chi_4), A005401 (Heisenberg).

E.g.f.: F(tanh(x)), where F(x) is the g.f. of A002906. - Andrey Zabolotskiy, Nov 19 2024

Name clarified, terms a(15) and beyond using data from A002906 added by Andrey Zabolotskiy, Nov 25 2024

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A010047 High-temperature expansion of Ising model susceptibility chi_4 for 4-d cubic lattice.

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

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A010039 High-temperature expansion of Ising model susceptibility chi_2 for square lattice.

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