A007207 Magnetization for hexagonal lattice.
1, 0, 0, -2, 0, -12, 2, -78, 24, -548, 228, -4050, 2030, -30960, 17670, -242402, 152520, -1932000, 1312844, -15612150, 11297052, -127551884, 97291026, -1051478274, 838994486, -8732657724, 7246304736, -72983051674, 62686156026, -613243234224, 543146222970
Offset: 0
References
- C. Domb, Ising model, in Phase Transitions and Critical Phenomena, vol. 3, ed. C. Domb and M. S. Green, Academic Press, 1974; p. 421.
- N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
Links
- C. Domb, Ising model, Phase Transitions and Critical Phenomena 3 (1974), 257, 380-381, 384-387, 390-391, 412-423. (Annotated scanned copy)
- Shigeo Naya, On the Spontaneous Magnetizations of Honeycomb and Kagomé Ising Lattices, Progress of Theoretical Physics, 11 (1954), 53-62.
- G. Nebe and N. J. A. Sloane, Home page for hexagonal (or triangular) lattice A2
Programs
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Mathematica
CoefficientList[Series[(1 - 16 * x^3 / ((1+3*x) * (1-x)^3))^(1/8), {x, 0, 30}], x] (* Vaclav Kotesovec, Apr 27 2024 *)
Formula
G.f.: (1 - 16 * x^3 / ((1+3*x) * (1-x)^3))^(1/8) [Shigeo Naya]. - Andrey Zabolotskiy, Jun 01 2022
a(n) ~ (-1)^n * 3^n / (Gamma(1/8) * 2^(1/4) * n^(7/8)) * (1 - (-1)^n * sqrt(sqrt(2) - 1) * Gamma(1/8)^2 / (2^(13/4) * Pi * n^(1/4))). - Vaclav Kotesovec, Apr 27 2024
Extensions
Offset changed, signs of terms changed, and more terms added by Andrey Zabolotskiy, Jun 01 2022
Comments