A002917 High temperature series for spin-1/2 Ising specific heat on 3-dimensional b.c.c. lattice.

4, 140, 4056, 129360, 4381848, 153700408, 5519859080, 201714989064

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• more

References

• 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).

Links

• G. A. Baker, Further application of the Padé approximant method to the Ising and Heisenberg models, Phys. Rev. 129 (1963) 99-102.
• Index entries for sequences related to b.c.c. lattice
• Index entries for sequences related to specific heat

Crossrefs

Cf. A002916 (cubic), A002918 (f.c.c.), A001406 (partition function), A047711 (internal energy), A002914 (susceptibility), A002167 (Heisenberg model).

Formula

Sum_{n>=0} a(n) * v^(2*n) = (v^2-1) * (-q/2*f(v)^2 - (v^2-1) * f'(v)^2 + f(v) * (2*v*f'(v) + (v^2-1)*f''(v))) / f(v)^2, where f(v) = Sum_{n>=0} A001406(n) * v^(2*n) and q = 8 is the number of nearest neighbors. - Andrey Zabolotskiy, Feb 15 2022

Extensions

Better description from Steven Finch

a(5)-a(7) from Andrey Zabolotskiy, Feb 15 2022