A242743 Decimal expansion of an Ising constant related to the random coloring problem.

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

Offset: 0

Author

Jean-François Alcover, Jun 02 2014

Keywords

• nonn
• cons

Comments

In Ising model on the 2D square lattice, the negated ratio of free energy per node to the temperature at the critical point. - Andrey Zabolotskiy, Sep 12 2017

Examples

			0.929695398341610214985384973665878...
		

References

• Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.22 Lenz-Ising constants, p. 399.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..10000
• Lars Onsager, Crystal Statistics. I. A Two-Dimensional Model with an Order-Disorder Transition, Phys. Rev. 65, 117 (1944) [see eq. (121)].

Crossrefs

Cf. A002898, A006752, A218387, A245592.

Programs

Magma

SetDefaultRealField(RealField(100)); R:=RealField(); Log(2)/2 + 2*Catalan(R)/Pi(R); // G. C. Greubel, Aug 25 2018

Mathematica

RealDigits[Log[2]/2 + 2*Catalan/Pi, 10, 105] // First

PARI

default(realprecision, 100); log(2)/2 + 2*Catalan/Pi \\ G. C. Greubel, Aug 25 2018

Formula

log(2)/2 + 2*G/Pi = log(2)/2 + A218387/2, where G is Catalan's constant.