A010039 -id:A010039 - cp's OEIS frontend

A010040 High-temperature expansion of Ising model susceptibility chi_2 for cubic lattice.

1, 6, 60, 888, 16944, 403296, 11342400, 371718528, 13814409984, 577113570816, 26660675466240, 1354001083680768, 74774085533159424, 4471493494982516736, 287295290091420794880, 19770508871470350532608, 1448690057046948138123264, 112756550398510017376813056

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. A002913, A010039 (square), A010041 (4D cubic), A010043 (mu_2), A010046 (chi_4), A002170 (Heisenberg).

E.g.f.: F(tanh(x)), where F(x) is the g.f. of A002913. - Andrey Zabolotskiy, Nov 19 2024

Name clarified, terms a(15) and beyond using data from A002913 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

cp's OEIS Frontend

A010040 High-temperature expansion of Ising model susceptibility chi_2 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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