cp's OEIS Frontend

A005399 E.g.f.: high-temperature series in J/2kT for ferromagnetic susceptibility for the spin-1/2 Heisenberg model on hexagonal lattice.

%I A005399 M4256 #33 Nov 25 2024 12:16:18
%S A005399 1,6,48,408,3600,42336,781728,13646016,90893568,-1798204416,
%T A005399 70794720768,7538546211840,63813109782528,-12977417912045568,
%U A005399 -320549902414196736,33016479733605777408,1709506241695601983488
%N A005399 E.g.f.: high-temperature series in J/2kT for ferromagnetic susceptibility for the spin-1/2 Heisenberg model on hexagonal lattice.
%C A005399 Previous name was: Susceptibility series for hexagonal lattice.
%C A005399 The hexagonal lattice is the familiar 2-dimensional lattice in which each point has 6 neighbors. This is sometimes called the triangular lattice.
%D A005399 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A005399 G. A. Baker Jr., H. E. Gilbert, J. Eve, and G. S. Rushbrooke, <a href="https://doi.org/10.1016/0375-9601(67)90860-2">On the two-dimensional, spin-1/2 Heisenberg ferromagnetic models</a>, Phys. Lett., 25A (1967), 207-209.
%H A005399 N. Elstner, R. R. P. Singh and A. P. Young, <a href="https://doi.org/10.1103/PhysRevLett.71.1629">Finite temperature properties of the spin-1/2 Heisenberg antiferromagnet on the triangular lattice</a>, Phys. Rev. Lett., 71 (1993), 1629-1632.
%H A005399 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 A005399 J. Oitmaa and E. Bornilla, <a href="https://doi.org/10.1103/PhysRevB.53.14228">High-temperature-series study of the spin-1/2 Heisenberg ferromagnet</a>, Phys. Rev. B, 53 (1996), 14228.
%H A005399 Laurent Pierre, Bernard Bernu and Laura Messio, <a href="https://doi.org/10.21468/SciPostPhys.17.4.105">High temperature series expansions of S = 1/2 Heisenberg spin models: Algorithm to include the magnetic field with optimized complexity</a>, SciPost Phys. 17, 105 (2024); arXiv:<a href="https://arxiv.org/abs/2404.02271">2404.02271</a> [cond-mat.str-el], 2024. See the supporting file <a href="https://bitbucket.org/lmessio/htse-coefficients/src/main/Triangle/Triangle_16_16.py">Triangle_16_16.py</a>; multiply pol1[1] by 2 to get this sequence.
%Y A005399 Cf. A002920 (Ising high-temperature), A047709 (Ising low-temperature), A005400 (series for specific heat, or free energy), A005401 (square lattice), A005402 (specific heat for square lattice).
%K A005399 sign,more
%O A005399 0,2
%A A005399 _N. J. A. Sloane_
%E A005399 New name from _Andrey Zabolotskiy_, Mar 03 2021
%E A005399 a(10)-a(12) added from Oitmaa and Bornilla by _Andrey Zabolotskiy_, Oct 20 2021
%E A005399 a(0) and a(13) using data from Elstner et al. (see Table I for the values -(-1)^n*n*a(n-1)) added by _Andrey Zabolotskiy_, Jun 17 2022
%E A005399 a(14)-a(16) using Pierre, Bernu & Messio's data added by _Andrey Zabolotskiy_, Nov 25 2024