A010564 -id:A010564 - cp's OEIS frontend

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

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

Offset: 0

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

A010367 High-temperature spin-1/2 Ising model series for second derivative of susceptibility with respect to magnetic field for hyper-body-centered-cubic lattice.

Original entry on oeis.org

2, 128, 9792, 886784, 92722944, 11014965248, 1465369976832, 215937597784064, 34916329300783104, 6147843514432913408, 1170908043876450435072

Offset: 1

N. J. A. Sloane

Moore defines two four-dimensional lattices called hbcc ("hyper-body-centered-cubic") and hfcc. They have essentially the same arrangement of sites, up to a similarity transformation. (That set of sites forms the D_4 lattice.) However the sets of bonds are different: each site of hfcc is connected to all 24 of its nearest neighbors, while each site of hbcc is connected only to 16 of them, specifically those which have relative position vector (+-1, +-1, +-1, +-1), but not (+-2, 0, 0, 0) or its permutations. - Andrey Zabolotskiy, Nov 26 2024

George A. Baker Jr. and John M. Kincaid, The continuous-spin Ising model, g0:phi4:d field theory and the renormalization group. J. Statist. Phys. 24 (1981), no. 3, 469-528. See Eq. (4.27).
M. A. Moore, Critical Behavior of the Four-Dimensional Ising Ferromagnet and the Breakdown of Scaling, Phys. Rev. B 1, 2238-2240 (1970).
Index entries for sequences related to D_4 lattice

Cf. A010047, A010559, A010560, A010564.

Edited by Andrey Zabolotskiy, Aug 01 2022 and Nov 26 2024

cp's OEIS Frontend

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

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