A010042 -id:A010042 - cp's OEIS frontend

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

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

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

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

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