A002169
High temperature series for spin-1/2 Heisenberg specific heat on 3-dimensional simple cubic lattice.
Original entry on oeis.org
0, 9, -18, -162, 2520, 33192, -1019088, -7804944, 723961728, 2596523904, -856142090496, 6383648984832, 1356696930401280, -27667884260938752, -2908030732698175488, 122264703581556307968, 7238339805811283361792
Offset: 1
- N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
- N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
- G. A. Baker et al., High-temperature expansions for the spin-1/2 Heisenberg model, Phys. Rev., 164 (1967), 800-817.
- C. Domb and D. Wood, On high-temperature expansions for the Heisenberg model, Proc. Physical Soc., 86 (1965), 1-16.
- M. G. Gonzalez, B. Bernu, L. Pierre and L. Messio, Finite-temperature phase transitions in S=1/2 three-dimensional Heisenberg magnets from high-temperature series expansions, Phys. Rev. B 107 (2023), 235151; arXiv:2303.03135 [cond-mat.str-el], 2023. See Table V; a_n = a(n)*(-1)^n.
- J. Oitmaa and E. Bornilla, High-temperature-series study of the spin-1/2 Heisenberg ferromagnet, Phys. Rev. B, 53 (1996), 14228. See Table I and the note added in proof.
- Index entries for sequences related to specific heat
- Index entries for sequences related to cubic lattice
a(11)-a(14) added from Oitmaa and Bornilla by
Andrey Zabolotskiy, Oct 20 2021 and Feb 05 2022
A005399
E.g.f.: high-temperature series in J/2kT for ferromagnetic susceptibility for the spin-1/2 Heisenberg model on hexagonal lattice.
Original entry on oeis.org
1, 6, 48, 408, 3600, 42336, 781728, 13646016, 90893568, -1798204416, 70794720768, 7538546211840, 63813109782528, -12977417912045568, -320549902414196736, 33016479733605777408, 1709506241695601983488
Offset: 0
- N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
- 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.
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).
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
A005401
High-temperature series for Heisenberg model susceptibility on square lattice.
Original entry on oeis.org
4, 16, 64, 416, 4544, 23488, -207616, 4205056, 198295552, -2574439424, -112886362112, 3567419838464, 94446596145152, -5636771173998592, -80736001427931136, 11035864514607054848, 15012780903941799936, -25650368909583695740928
Offset: 1
- N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
- G. A. Baker Jr., H. E. Gilbert, J. Eve, G. S. Rushbrooke, On the two-dimensional, spin-1/2 Heisenberg ferromagnetic models, Phys. Lett., 25A (1967), 207-209.
- J. Oitmaa and E. Bornilla, High-temperature-series study of the spin-1/2 Heisenberg ferromagnet, Phys. Rev. B, 53 (1996), 14228. See Table I and the note added in proof.
- 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 Square_18_1.py; multiply pol1[1] by 2 to get this sequence.
Terms a(11)-a(14) added from Oitmaa and Bornilla by
Andrey Zabolotskiy, Oct 20 2021 and Feb 05 2022
Name clarified, terms a(15)-a(18) using Pierre, Bernu & Messio's data added by
Andrey Zabolotskiy, Nov 25 2024
A005400
High temperature series for spin-1/2 Heisenberg specific heat on 2D hexagonal lattice.
Original entry on oeis.org
0, 9, 18, -306, -3240, 49176, 1466640, -13626000, -1172668032, 75256704, 1392243773184, 18426692664576, -2213592367094784, -74200148173310976, 4271973657228822528, 294089252618987845632, -8526609981314268364800, -1299100041545138822873088
Offset: 1
- N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
- 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_18_0.py.
- Index entries for sequences related to specific heat
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
Showing 1-4 of 4 results.
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