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A002920
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High-temperature series in w = tanh(J/kT) for ferromagnetic susceptibility for the spin-1/2 Ising model on hexagonal lattice.
(Formerly M4196 N1750)
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5
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1, 6, 30, 138, 606, 2586, 10818, 44574, 181542, 732678, 2935218, 11687202, 46296210, 182588850, 717395262, 2809372302, 10969820358, 42724062966, 166015496838, 643768299018, 2491738141314, 9628130289018, 37146098272266, 143110933254702, 550643544948090
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OFFSET
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0,2
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COMMENTS
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Previous name was: Susceptibility series for hexagonal lattice.
The hexagonal lattice is the familiar 2-dimensional lattice in which each point has 6 neighbors. This is sometimes called the triangular lattice.
The actual susceptibility per spin is this series times m^2/kT. (m is the magnetic moment of a single spin; this factor may be present or absent depending on the precise definition of the susceptibility.)
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REFERENCES
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C. Domb, Ising model, in Phase Transitions and Critical Phenomena, vol. 3, ed. C. Domb and M. S. Green, Academic Press, 1974; p. 380.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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C. Domb, Ising model, Phase Transitions and Critical Phenomena 3 (1974), 257, 380-381, 384-387, 390-391, 412-423. (Annotated scanned copy)
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FORMULA
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G.f.: (h(v(w)) + h(-v(w))) / 2, where h(v) is the g.f. of A002910 and v(w)^2 = w*(1+w)/(1+w^3) [Fisher, p. 979]. - Andrey Zabolotskiy, Mar 01 2021
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CROSSREFS
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KEYWORD
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nonn,nice
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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