A245592 Decimal expansion of the Ising constant K_c, the ratio of the coupling constant to the ferromagnetic critical temperature, in the two-dimensional case.

4, 4, 0, 6, 8, 6, 7, 9, 3, 5, 0, 9, 7, 7, 1, 5, 1, 2, 6, 1, 6, 3, 0, 4, 6, 6, 2, 4, 8, 9, 8, 9, 6, 1, 5, 4, 5, 1, 4, 0, 8, 0, 1, 6, 4, 1, 3, 0, 8, 1, 7, 7, 0, 5, 3, 7, 6, 6, 4, 7, 8, 0, 4, 3, 2, 6, 6, 8, 8, 5, 9, 2, 1, 1, 1, 0, 1, 3, 0, 4, 3, 9, 1, 6, 8, 5, 3, 4, 4, 5, 9, 5, 5, 1, 2, 8, 0, 2, 1, 4, 2, 8

Offset

0,1

References

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.22 Lenz-Ising Constants, p. 396.

Links

Table of n, a(n) for n=0..101.

Andrei Okounkov, Limit shapes, real and imagined, Bull. Amer. Math. Soc. 53 2 (2016), 187-216

Wikipedia, Ising Model.

Formula

K_c = (1/2)*log(1 + sqrt(2)) = (1/2)*A091648.

Equals Integral_{0..1} x/sqrt(1 + x^4) dx. - Peter Bala, Oct 28 2019

Equals arcsinh(1)/2. - Peter Luschny, Oct 29 2019

Equals arctanh(sqrt(2)-1). - Amiram Eldar, Feb 09 2024

Example

0.4406867935097715126163046624898961545140801641308177053766478...

Mathematica

RealDigits[(1/2)*Log[1 + Sqrt[2]], 10, 102] // First

Crossrefs

Cf. A091648.

Sequence in context: A155502 A228048 A016705 * A169783 A133657 A121455

Adjacent sequences: A245589 A245590 A245591 * A245593 A245594 A245595

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Jul 30 2014

Status

approved