A370955 - OEIS

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.

%I #23 Apr 28 2024 18:07:08

%S 1,-1,-4,-29,-265,-2745,-30773,-364315,-4488749,-57020414,-741999700,

%T -9845906898,-132774990781,-1814964497342,-25098172218816,

%U -350548840292011,-4938909144117611,-70118741489312657,-1002259422501603334,-14412940220878338617,-208393139882994584383

%N 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 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 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 Hendrik A. Kramers and Gregory H. Wannier, <a href="/A370955/a370955.pdf">Extract 1 from page 264 of Part II.</a>

%H Hendrik A. Kramers and Gregory H. Wannier, <a href="/A370955/a370955_1.pdf">Extract 2 from page 264 of Part II.</a>

%H 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 Wikipedia, <a href="https://en.wikipedia.org/wiki/Square_lattice_Ising_model">Square lattice Ising model</a>.

%F From _Vaclav Kotesovec_, Apr 28 2024: (Start)

%F a(n) ~ -c * 16^n / n^2, where c = 0.071286406...

%F Conjecture: c = exp(2*G/Pi)/(8*Pi) = 0.071286406674269408358123..., where G is the Catalan's constant A006752. (End)

%t 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 Cf. A002890, A370953, A370954.

%K sign,easy

%O 0,3

%A _N. J. A. Sloane_, Mar 10 2024

%E Terms a(6) and beyond from _Andrey Zabolotskiy_, Mar 10 2024