A010557 -id:A010557 - 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

A010572 High-temperature coefficients for the internal energy for spin-1/2 Ising model on 4-d cubic lattice.

Original entry on oeis.org

4, 24, 432, 10512, 290552, 8800432, 284289160, 9621738448

Offset: 0

N. J. A. Sloane

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.

Cf. A010571 (3D), A010573 (5D), A010574 (6D), A030044 (partition function), A010557 (fourth-field derivative of free energy), A010563.

Sum_{n>=0} a(n) * v^(2*n+1) = v*q/2 + (1-v^2) * f'(v) / f(v), where f(v) = Sum_{n>=0} A030044(n) * v^(2*n) and q = 8 is the number of nearest neighbors. - Andrey Zabolotskiy, Feb 16 2022

a(5)-a(7) from Andrey Zabolotskiy, Feb 16 2022, corrected Nov 26 2024

A010563 High-temperature expansion for Ising model spin-spin correlation function on 4-d cubic lattice.

Original entry on oeis.org

1, 6, 108, 2628, 72638, 2200108, 71072290, 2405434612

Offset: 0

N. J. A. Sloane

M. A. Moore, Critical behavior of the four-dimensional Ising ferromagnet and the breakdown of scaling, Phys. Rev. B 1 (1970), 2238-2240.

Cf. A010572, A030044 (partition function), A010557 (fourth-field derivative of free energy); A010564 ("HBCC" lattice), A010565 (D_4 lattice).

a(n) = A010572(n) / 4. - Andrey Zabolotskiy, Nov 19 2024

Name clarified and terms a(6)-a(7) using data from A010572 added by Andrey Zabolotskiy, Nov 25 2024

cp's OEIS Frontend

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

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A010572 High-temperature coefficients for the internal energy for spin-1/2 Ising model on 4-d cubic lattice.

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A010563 High-temperature expansion for Ising model spin-spin correlation function on 4-d cubic lattice.

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Author

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Formula

Extensions