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

Author

Jean-François Alcover, Jul 30 2014

Keywords

• nonn
• cons
• easy

Examples

			0.4406867935097715126163046624898961545140801641308177053766478...
		

References

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

Links

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

Crossrefs

Cf. A091648.

Programs

Mathematica

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

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