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A002916 High temperature series for spin-1/2 Ising specific heat on 3-dimensional simple cubic lattice.
(Formerly M3133 N1271)
5

%I M3133 N1271 #41 Feb 15 2022 13:58:32

%S 3,33,564,8976,155124,2791308,51382068,962178084,18258531348,

%T 350143322088,6772382631732,131922552534036,2585198190891636,

%U 50919899448451512,1007393565758096820,20007153991627682124,398699967207692643924,7969220499183448073760,159718349893920279061428

%N High temperature series for spin-1/2 Ising specific heat on 3-dimensional simple cubic lattice.

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

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H G. A. Baker, <a href="https://doi.org/10.1103/PhysRev.129.99">Further application of the Padé approximant method to the Ising and Heisenberg models</a>, Phys. Rev. 129 (1963) 99-102.

%H Steven R. Finch, <a href="http://www.people.fas.harvard.edu/~sfinch/constant/ising/ising.html">Lenz-Ising Constants</a> [broken link]

%H Steven R. Finch, <a href="http://web.archive.org/web/20010207201511/http://www.mathsoft.com:80/asolve/constant/ising/ising.html">Lenz-Ising Constants</a> [From the Wayback Machine]

%H A. J. Guttmann and I. G. Enting, <a href="https://doi.org/10.1088/0305-4470/27/24/012">The high-temperature specific heat exponent of the 3-dimensional Ising model</a>, J. Phys. A 27 (1994) 8007-8010.

%H <a href="/index/Sp#specific_heat">Index entries for sequences related to specific heat</a>

%F 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

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

%Y Equals 3*A001408.

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

%K nonn

%O 0,1

%A _N. J. A. Sloane_

%E Corrections and updates from _Steven Finch_

%E Terms a(13) and beyond from _Andrey Zabolotskiy_, Feb 15 2022

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)