A002916 High temperature series for spin-1/2 Ising specific heat on 3-dimensional simple cubic lattice.
3, 33, 564, 8976, 155124, 2791308, 51382068, 962178084, 18258531348, 350143322088, 6772382631732, 131922552534036, 2585198190891636, 50919899448451512, 1007393565758096820, 20007153991627682124, 398699967207692643924, 7969220499183448073760, 159718349893920279061428
Offset: 0
Keywords
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
- 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
Crossrefs
Programs
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Mathematica
3 Cases[Import["https://oeis.org/A001408/b001408.txt", "Table"], {, }][[All, 2]] (* Jean-François Alcover, Jan 17 2020 *)
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
Extensions
Corrections and updates from Steven Finch
Terms a(13) and beyond from Andrey Zabolotskiy, Feb 15 2022