A002918 High temperature series for spin-1/2 Ising specific heat on 3-dimensional f.c.c. lattice.

6, 48, 390, 3216, 26844, 229584, 2006736, 17809008, 159799812, 1446245424, 13181330772, 120849559824, 1113598633188

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.
• A. J. Guttmann and G. S. Joyce, Critical behaviour of an isotropic spin system, J. Phys. C: Solid State Phys., 6 (1973), 2691-2712. See Table 1.
• Index entries for sequences related to f.c.c. lattice
• Index entries for sequences related to specific heat

Crossrefs

Cf. A002916 (cubic), A002917 (b.c.c.), A002921 (susceptibility), A001407 (partition function), A002165 (Heisenberg).

Formula

G.f.: (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) is the g.f. of A001407 and q = 12 is the number of nearest neighbors. - Andrey Zabolotskiy, Feb 15 2022

Extensions

Better description from Steven Finch

a(8)-a(10) from Guttmann & Joyce added by Andrey Zabolotskiy, Feb 02 2022

a(11)-a(12) from Andrey Zabolotskiy, Feb 15 2022