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.

1, -1, -4, -29, -265, -2745, -30773, -364315, -4488749, -57020414, -741999700, -9845906898, -132774990781, -1814964497342, -25098172218816, -350548840292011, -4938909144117611, -70118741489312657, -1002259422501603334, -14412940220878338617, -208393139882994584383

Offset

0,3

Links

Table of n, a(n) for n=0..20.

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 (45), p. 264.

Hendrik A. Kramers and Gregory H. Wannier, Extract 1 from page 264 of Part II.

Hendrik A. Kramers and Gregory H. Wannier, Extract 2 from page 264 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.

Wikipedia, Square lattice Ising model.

Formula

From Vaclav Kotesovec, Apr 28 2024: (Start)

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

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

Mathematica

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 *)

Crossrefs

Cf. A002890, A370953, A370954.

Sequence in context: A369215 A244594 A168238 * A294160 A160885 A182356

Adjacent sequences: A370952 A370953 A370954 * A370956 A370957 A370958

Keyword

sign,easy

Author

N. J. A. Sloane, Mar 10 2024

Extensions

Terms a(6) and beyond from Andrey Zabolotskiy, Mar 10 2024

Status

approved