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A370953
Numerators of coefficients of the partition function per spin, lambda (divided by 2), in the very high temperature region, expressed as a power series in the parameter K^2, for the spin-1/2 Ising model on square lattice.
3
1, 1, 4, 77, 1009, 101627, 1302779, 2513121979, 11291682179, 1354947005798, 23064317580681848, 20189102649892270054, 776220757551441546419, 641273428219629914673014, 5433381672262390009892530636, 1399751922597075578762073697769
OFFSET
0,3
LINKS
Hendrik A. Kramers and Gregory H. Wannier. Statistics of the two-dimensional ferromagnet. Part I. Phys. Rev. 60 (1941), 252-262.
Hendrik A. Kramers and Gregory H. Wannier. Statistics of the two-dimensional ferromagnet. Part II. Phys. Rev. 60 (1941), 263-276. See (41), p. 263.
Hendrik A. Kramers and Gregory H. Wannier, Extract from page 263 of Part II.
Gandhimohan M. Viswanathan, The hypergeometric series for the partition function of the 2D Ising model, J. Stat. Mech. (2015) P07004; arXiv:1411.2495 [cond-mat.stat-mech], 2014-2015.
FORMULA
a(n) / A370954(n) ~ c * 2^(2*n) / (n^3 * log(1 + sqrt(2))^(2*n)), where c = 0.15662885... - Vaclav Kotesovec, May 02 2024
MATHEMATICA
CoefficientList[With[{nmax = 7}, Exp[-Log[2]/2 + 1/(2 Pi) Integrate[Log[Cosh[2k]^2 + Sqrt[Sinh[2k]^4 + 1 - 2 Sinh[2k]^2 Cos[2\[Theta]] + O[k]^(2nmax+1)]], {\[Theta], 0, Pi}] + O[k]^(2nmax+1)]], k][[;; ;; 2]] // Numerator (* Andrey Zabolotskiy, Mar 10 2024 *)
CoefficientList[Cosh[2k] Exp[-x HypergeometricPFQ[{1, 1, 3/2, 3/2}, {2, 2, 2}, 16x] /. {x -> (Sinh[2k]/(2Cosh[2k]^2))^2}] + O[k]^32, k][[;; ;; 2]] // Numerator (* Andrey Zabolotskiy, Mar 13 2024, using the g. f. from Gandhimohan M. Viswanathan *)
CROSSREFS
See A370954 for denominators.
Sequence in context: A080989 A006267 A273952 * A201984 A210519 A279437
KEYWORD
nonn,frac
AUTHOR
N. J. A. Sloane, Mar 10 2024
EXTENSIONS
Terms a(5) and beyond from Andrey Zabolotskiy, Mar 10 2024
STATUS
approved