%I N2061 #15 Feb 11 2022 17:15:03
%S 0,0,1,0,12,4,129,72,1332,960,13419,11372,132900,126396,1299851,
%T 1349784,12592440,14023944,121074183,142818336,1157026804,1432470300,
%U 11001347199,14196860272,104161648860,139351826712,982653092725,1357030991292,9241395939636
%N Low-temperature series in u = exp(-4J/kT) for ferromagnetic susceptibility for the spin-1/2 Ising model on 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 Many sources give this sequence multiplied by 4 because the actual susceptibility per spin is this series times 4m^2/kT. (m is the magnetic moment of a single spin; the factor m^2 may be present or absent depending on the precise definition of the susceptibility.)
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (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 642 terms in the file Triangle_u642.txt (divide by 4 to get this sequence).
%H J. W. Essam and M. E. Fisher, <a href="https://doi.org/10.1063/1.1733766">Padé approximant studies of the lattice gas and Ising ferromagnet below the critical point</a>, J. Chem. Phys., 38 (1963), 802-812.
%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 and M. E. Fisher, <a href="https://doi.org/10.1016/0031-8914(62)90080-0">Antiferromagnetic susceptibility of the plane square and honeycomb Ising lattices</a>, Physica, 28 (1962), 919-938.
%H M. F. Sykes, D. S. Gaunt, J. L. Martin, S. R. Mattingly, and J. W. Essam, <a href="https://doi.org/10.1063/1.1666439">Derivation of low‐temperature expansions for Ising model. IV. Two‐dimensional lattices‐temperature grouping</a>, Journal of Mathematical Physics 14 (1973), 1071.
%Y Cf. A002919, A002920, A003488, A005399, A057383, A057387.
%Y Cf. A002912, A002927, A002924, A002925, A002926, A003220.
%K nonn,nice
%O 1,5
%A _N. J. A. Sloane_
%E Edited and extended from Chan et al by _Andrey Zabolotskiy_, Mar 02 2021