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%I M4196 N1750 #32 Feb 11 2022 08:41:06
%S 1,6,30,138,606,2586,10818,44574,181542,732678,2935218,11687202,
%T 46296210,182588850,717395262,2809372302,10969820358,42724062966,
%U 166015496838,643768299018,2491738141314,9628130289018,37146098272266,143110933254702,550643544948090
%N High-temperature series in w = tanh(J/kT) for ferromagnetic susceptibility for the spin-1/2 Ising model on hexagonal lattice.
%C Previous name was: Susceptibility series for hexagonal lattice.
%C The hexagonal lattice is the familiar 2-dimensional lattice in which each point has 6 neighbors. This is sometimes called the triangular lattice.
%C 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.)
%D C. Domb, Ising model, in Phase Transitions and Critical Phenomena, vol. 3, ed. C. Domb and M. S. Green, Academic Press, 1974; p. 380.
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Y. Chan, A. J. Guttmann, B. G. Nickel, and J. H. H. Perk, <a href="https://doi.org/10.1007/s10955-011-0212-0">The Ising Susceptibility Scaling Function</a>, J Stat Phys 145 (2011), 549-590; arXiv:<a href="https://arxiv.org/abs/1012.5272">1012.5272</a> [cond-mat.stat-mech], 2010-2020. Gives 320 terms in the file Triangle_v319.
%H C. Domb, <a href="/A007239/a007239.pdf">Ising model</a>, Phase Transitions and Critical Phenomena 3 (1974), 257, 380-381, 384-387, 390-391, 412-423. (Annotated scanned copy)
%H Michael E. Fisher, <a href="https://doi.org/10.1103/PhysRev.113.969">Transformations of Ising Models</a>, Phys. Rev. 113 (1959), 969-981.
%H M. E. Fisher and R. J. Burford, <a href="https://doi.org/10.1103/PhysRev.156.583">Theory of critical point scattering and correlations I: the Ising model</a>, Phys. Rev. 156 (1967), 583-621.
%H G. Nebe and N. J. A. Sloane, <a href="http://www.math.rwth-aachen.de/~Gabriele.Nebe/LATTICES/A2.html">Home page for hexagonal (or triangular) lattice A2</a>
%H M. F. Sykes, <a href="https://doi.org/10.1063/1.1724212">Some counting theorems in the theory of the Ising problem and the excluded volume problem</a>, J. Math. Phys., 2 (1961), 52-62.
%H M. F. Sykes, D. G. Gaunt, P. D. Roberts and J. A. Wyles, <a href="https://doi.org/10.1088/0305-4470/5/5/004">High temperature series for the susceptibility of the Ising model, I. Two dimensional lattices</a>, J. Phys. A 5 (1972) 624-639.
%F 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
%Y Cf. A002910, A128834, A047709, A002919.
%K nonn,nice
%O 0,2
%A _N. J. A. Sloane_
%E Edited and extended from Chan et al by _Andrey Zabolotskiy_, Mar 03 2021
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