A002916 High temperature series for spin-1/2 Ising specific heat on 3-dimensional simple cubic lattice. (Formerly M3133 N1271)

3, 33, 564, 8976, 155124, 2791308, 51382068, 962178084, 18258531348, 350143322088, 6772382631732, 131922552534036, 2585198190891636, 50919899448451512, 1007393565758096820, 20007153991627682124, 398699967207692643924, 7969220499183448073760, 159718349893920279061428

Offset

0,1

References

S. R. Finch, Mathematical Constants, Cambridge, 2003, pp. 391-406.

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

Table of n, a(n) for n=0..18.

G. A. Baker, Further application of the Padé approximant method to the Ising and Heisenberg models, Phys. Rev. 129 (1963) 99-102.

Steven R. Finch, Lenz-Ising Constants [broken link]

Steven R. Finch, Lenz-Ising Constants [From the Wayback Machine]

A. J. Guttmann and I. G. Enting, The high-temperature specific heat exponent of the 3-dimensional Ising model, J. Phys. A 27 (1994) 8007-8010.

Index entries for sequences related to specific heat

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} A001393(n) * v^(2*n) and q = 6 is the number of nearest neighbors. - Andrey Zabolotskiy, Feb 15 2022

Mathematica

3 Cases[Import["https://oeis.org/A001408/b001408.txt", "Table"], {_, _}][[All, 2]] (* Jean-François Alcover, Jan 17 2020 *)

Crossrefs

Equals 3*A001408.

Cf. A002917 (b.c.c.), A002918 (f.c.c.), A001393 (partition function), A010571 (internal energy), A002913 (susceptibility), A002169 (Heisenberg model), A029872 (square, low-temperature).

Sequence in context: A209245 A092170 A083080 * A009659 A367427 A361212

Adjacent sequences: A002913 A002914 A002915 * A002917 A002918 A002919

Keyword

nonn

Author

N. J. A. Sloane

Extensions

Corrections and updates from Steven Finch

Terms a(13) and beyond from Andrey Zabolotskiy, Feb 15 2022

Status

approved