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

1, 6, 48, 408, 3600, 42336, 781728, 13646016, 90893568, -1798204416, 70794720768, 7538546211840, 63813109782528, -12977417912045568, -320549902414196736, 33016479733605777408, 1709506241695601983488

Offset: 0

Author

N. J. A. Sloane

Keywords

• sign
• more

Comments

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.

References

• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• G. A. Baker Jr., H. E. Gilbert, J. Eve, and G. S. Rushbrooke, On the two-dimensional, spin-1/2 Heisenberg ferromagnetic models, Phys. Lett., 25A (1967), 207-209.
• N. Elstner, R. R. P. Singh and A. P. Young, Finite temperature properties of the spin-1/2 Heisenberg antiferromagnet on the triangular lattice, Phys. Rev. Lett., 71 (1993), 1629-1632.
• G. Nebe and N. J. A. Sloane, Home page for hexagonal (or triangular) lattice A2
• J. Oitmaa and E. Bornilla, High-temperature-series study of the spin-1/2 Heisenberg ferromagnet, Phys. Rev. B, 53 (1996), 14228.
• Laurent Pierre, Bernard Bernu and Laura Messio, High temperature series expansions of S = 1/2 Heisenberg spin models: Algorithm to include the magnetic field with optimized complexity, SciPost Phys. 17, 105 (2024); arXiv:2404.02271 [cond-mat.str-el], 2024. See the supporting file Triangle_16_16.py; multiply pol1[1] by 2 to get this sequence.

Crossrefs

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).

Extensions

New name from Andrey Zabolotskiy, Mar 03 2021

a(10)-a(12) added from Oitmaa and Bornilla by Andrey Zabolotskiy, Oct 20 2021

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

a(14)-a(16) using Pierre, Bernu & Messio's data added by Andrey Zabolotskiy, Nov 25 2024