cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A370955 Coefficients of the partition function per spin, x(k) (divided by 2), in the low temperature region, expressed as a power series in the parameter k^2, for the spin-1/2 Ising model on square lattice.

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%I A370955 #23 Apr 28 2024 18:07:08
%S A370955 1,-1,-4,-29,-265,-2745,-30773,-364315,-4488749,-57020414,-741999700,
%T A370955 -9845906898,-132774990781,-1814964497342,-25098172218816,
%U A370955 -350548840292011,-4938909144117611,-70118741489312657,-1002259422501603334,-14412940220878338617,-208393139882994584383
%N A370955 Coefficients of the partition function per spin, x(k) (divided by 2), in the low temperature region, expressed as a power series in the parameter k^2, for the spin-1/2 Ising model on square lattice.
%H A370955 Hendrik A. Kramers and Gregory H. Wannier. <a href="https://doi.org/10.1103/PhysRev.60.252">Statistics of the two-dimensional ferromagnet. Part I</a>. Phys. Rev. 60 (1941), 252-262.
%H A370955 Hendrik A. Kramers and Gregory H. Wannier. <a href="https://doi.org/10.1103/PhysRev.60.263">Statistics of the two-dimensional ferromagnet. Part II</a>. Phys. Rev. 60 (1941), 263-276. See (45), p. 264.
%H A370955 Hendrik A. Kramers and Gregory H. Wannier, <a href="/A370955/a370955.pdf">Extract 1 from page 264 of Part II.</a>
%H A370955 Hendrik A. Kramers and Gregory H. Wannier, <a href="/A370955/a370955_1.pdf">Extract 2 from page 264 of Part II.</a>
%H A370955 Gandhimohan M. Viswanathan, <a href="http://doi.org/10.1088/1742-5468/2015/07/P07004">The hypergeometric series for the partition function of the 2D Ising model</a>, J. Stat. Mech. (2015) P07004; arXiv:<a href="http://arxiv.org/abs/1411.2495">1411.2495</a> [cond-mat.stat-mech], 2014-2015.
%H A370955 Wikipedia, <a href="https://en.wikipedia.org/wiki/Square_lattice_Ising_model">Square lattice Ising model</a>.
%F A370955 From _Vaclav Kotesovec_, Apr 28 2024: (Start)
%F A370955 a(n) ~ -c * 16^n / n^2, where c = 0.071286406...
%F A370955 Conjecture: c = exp(2*G/Pi)/(8*Pi) = 0.071286406674269408358123..., where G is the Catalan's constant A006752. (End)
%t A370955 CoefficientList[Exp[-x HypergeometricPFQ[{1, 1, 3/2, 3/2}, {2, 2, 2}, 16 x]] + O[x]^20, x] (* _Andrey Zabolotskiy_, Mar 10 2024, using the g. f. from Gandhimohan M. Viswanathan *)
%Y A370955 Cf. A002890, A370953, A370954.
%K A370955 sign,easy
%O A370955 0,3
%A A370955 _N. J. A. Sloane_, Mar 10 2024
%E A370955 Terms a(6) and beyond from _Andrey Zabolotskiy_, Mar 10 2024