cp's OEIS Frontend

A005400 High temperature series for spin-1/2 Heisenberg specific heat on 2D hexagonal lattice.

%I A005400 M4603 #39 Nov 25 2024 12:16:04
%S A005400 0,9,18,-306,-3240,49176,1466640,-13626000,-1172668032,75256704,
%T A005400 1392243773184,18426692664576,-2213592367094784,-74200148173310976,
%U A005400 4271973657228822528,294089252618987845632,-8526609981314268364800,-1299100041545138822873088
%N A005400 High temperature series for spin-1/2 Heisenberg specific heat on 2D hexagonal lattice.
%C A005400 The hexagonal lattice is the familiar 2-dimensional lattice in which each point has 6 neighbors. This is sometimes called the triangular lattice.
%D A005400 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A005400 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 A005400 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 A005400 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 A005400 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 A005400 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_18_0.py">Triangle_18_0.py</a>.
%H A005400 <a href="/index/Sp#specific_heat">Index entries for sequences related to specific heat</a>
%Y A005400 Cf. A005399 (susceptibility), A005402 (square lattice).
%K A005400 sign
%O A005400 1,2
%A A005400 _N. J. A. Sloane_
%E A005400 Better description from _Steven Finch_
%E A005400 a(11)-a(12) added from Oitmaa and Bornilla by _Andrey Zabolotskiy_, Oct 20 2021
%E A005400 a(13) from Elstner et al. (see table I; signs differ because they consider antiferromagnet, and they mention energy instead of specific heat because the same coefficients are involved, cf. Eqs. (11) and (13) from Oitmaa & Bornilla) added by _Andrey Zabolotskiy_, Jun 17 2022
%E A005400 a(14)-a(18) from Pierre, Bernu & Messio added by _Andrey Zabolotskiy_, Nov 25 2024