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

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

Offset

0,1

Links

Table of n, a(n) for n=0..7.

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.

Formula

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

Crossrefs

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

Sequence in context: A185457 A024250 A167140 * A247737 A326871 A012945

Adjacent sequences: A010569 A010570 A010571 * A010573 A010574 A010575

Keyword

nonn,more

Author

N. J. A. Sloane

Extensions

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

Status

approved