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A002890 Low temperature series for spin-1/2 Ising free energy on 2D square lattice.
(Formerly M1463 N0578)
2
1, 0, 1, 2, 5, 14, 44, 152, 566, 2234, 9228, 39520, 174271, 787246, 3628992, 17019374, 81011889, 390633382, 1905134695, 9385453576, 46653815395, 233788460256, 1180111379105, 5996452414310, 30653752894948 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

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..24.

P. D. Beale, Exact distribution of energies in the two-dimensional Ising model, Phys. Rev. Lett. 76 (1996) 78-81

C. Domb, On the theory of cooperative phenomena in crystals, Advances in Phys., 9 (1960), 149-361.

S. R. Finch, Lenz-Ising Constants

G. Siudem, A. Fronczak, P. Fronczak, Exact low-temperature series expansion for the partition function of the two-dimensional zero-field s= 1/2 Ising model on the infinite square lattice, arXiv preprint arXiv:1410.7963 [math-ph], 2014-2015.

Gandhimohan M. Viswanathan, The hypergeometric series for the partition function of the 2-D Ising model arXiv:1411.2495 [cond-mat.stat-mech], 2014-2015.

MATHEMATICA

(* For 25 terms, a PC computation lasts less than half an hour *) m = 48 (* max y exponent *); coes = CoefficientList[ Series[ Log[(1 + y^2)^2 - 2*y*(1 - y^2)*(Cos[2*Pi*u] + Cos[2*Pi*v])], {y, 0, m}], y] // Rest; nint[f_, {n_}] := If[n == 2 || OddQ[n], 0, Print[n]; Integrate[ Integrate[f, {u, 0, 1}], {v, 0, 1}]]; fy = MapIndexed[nint, coes].Table[y^k, {k, 1, m}]; CoefficientList[ Series[ Exp[fy/2], {y, 0, m}] , y^2] (* Jean-Fran├žois Alcover, Mar 19 2013 *)

CROSSREFS

Sequence in context: A148336 A257273 A119021 * A202856 A118929 A287252

Adjacent sequences:  A002887 A002888 A002889 * A002891 A002892 A002893

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

EXTENSIONS

Corrections and updates from Steven Finch

STATUS

approved

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Last modified January 17 00:44 EST 2019. Contains 319206 sequences. (Running on oeis4.)