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A242743
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Decimal expansion of an Ising constant related to the random coloring problem.
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2
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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
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OFFSET
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0,1
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COMMENTS
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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
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REFERENCES
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Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.22 Lenz-Ising constants, p. 399.
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LINKS
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FORMULA
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log(2)/2 + 2*G/Pi = log(2)/2 + A218387/2, where G is Catalan's constant.
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EXAMPLE
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0.929695398341610214985384973665878...
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MATHEMATICA
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RealDigits[Log[2]/2 + 2*Catalan/Pi, 10, 105] // First
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PROG
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(PARI) default(realprecision, 100); log(2)/2 + 2*Catalan/Pi \\ G. C. Greubel, Aug 25 2018
(Magma) SetDefaultRealField(RealField(100)); R:=RealField(); Log(2)/2 + 2*Catalan(R)/Pi(R); // G. C. Greubel, Aug 25 2018
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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