cp's OEIS Frontend

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.

%I A245592 #29 Feb 09 2024 03:26:19
%S A245592 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,
%T A245592 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,
%U A245592 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
%N 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.
%D A245592 Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.22 Lenz-Ising Constants, p. 396.
%H A245592 Andrei Okounkov, <a href="https://doi.org/10.1090/bull/1512">Limit shapes, real and imagined</a>, Bull. Amer. Math. Soc. 53 2 (2016), 187-216
%H A245592 Wikipedia, <a href="http://en.wikipedia.org/wiki/Ising_model">Ising Model</a>.
%F A245592 K_c = (1/2)*log(1 + sqrt(2)) = (1/2)*A091648.
%F A245592 Equals Integral_{0..1} x/sqrt(1 + x^4) dx. - _Peter Bala_, Oct 28 2019
%F A245592 Equals arcsinh(1)/2. - _Peter Luschny_, Oct 29 2019
%F A245592 Equals arctanh(sqrt(2)-1). - _Amiram Eldar_, Feb 09 2024
%e A245592 0.4406867935097715126163046624898961545140801641308177053766478...
%t A245592 RealDigits[(1/2)*Log[1 + Sqrt[2]], 10, 102] // First
%Y A245592 Cf. A091648.
%K A245592 nonn,cons,easy
%O A245592 0,1
%A A245592 _Jean-François Alcover_, Jul 30 2014