A002906 -id:A002906 - 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

A002907 High temperature series in v = tanh(J/kT) for residual correlation function (correction to susceptibility) for the spin-1/2 Ising model on square lattice.

Original entry on oeis.org

2, 2, 20, 38, 146, 368, 1070, 2824, 7680, 19996, 53024, 136350, 355254, 906254, 2331416, 5909810, 15067236, 37992680, 96210436, 241564514, 608469654, 1522388638, 3818281784, 9525139886, 23806217352, 59237754234, 147621207142, 366533832540, 911151508282

Offset: 0

N. J. A. Sloane

nonn

Previous name was: Susceptibility for square lattice.

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 and M. E. Fisher, Antiferromagnetic susceptibility of the plane square and honeycomb Ising lattices, Physica, 28 (1962), 919-938.

Cf. A002906, A002908.

G.f.: ((1-3*v)^2*xi(v) - (1-v)^2 + 2*v*u(v)) / (8*v^7*(1+v)^2), where xi(v) is the g.f. of A002906 and u(v) is the g.f. of A002908 (odd powers only!); the actual "residual correlation function" is the numerator of this expression [Sykes & Fisher]. - Andrey Zabolotskiy, Feb 28 2021

New name and terms a(10) and beyond from Andrey Zabolotskiy, Feb 28 2021

cp's OEIS Frontend

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

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

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A002907 High temperature series in v = tanh(J/kT) for residual correlation function (correction to susceptibility) for the spin-1/2 Ising model on square lattice.

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