A002167 -id:A002167 - cp's OEIS frontend

A002169 High temperature series for spin-1/2 Heisenberg specific heat on 3-dimensional simple cubic lattice.

0, 9, -18, -162, 2520, 33192, -1019088, -7804944, 723961728, 2596523904, -856142090496, 6383648984832, 1356696930401280, -27667884260938752, -2908030732698175488, 122264703581556307968, 7238339805811283361792

Offset: 1

N. J. A. Sloane

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

Cf. A002165 (f.c.c.), A002167 (b.c.c.), A002922 (diamond), A005402 (square), A005402 (hexagonal); A002170 (susceptibility); A002916 (Ising).

Better description from Steven Finch
a(11)-a(14) added from Oitmaa and Bornilla by Andrey Zabolotskiy, Oct 20 2021 and Feb 05 2022
a(15)-a(17) added from Gonzalez et al. by Andrey Zabolotskiy, May 06 2023

A002165 High temperature series for spin-1/2 Heisenberg specific heat on 3-dimensional f.c.c. lattice.

Original entry on oeis.org

0, 18, 108, 180, -5040, 162000, 14565600, 563253408, 17544639744, 750412309248, 56646776913408, 4973976625190400, 421817449494804480

Offset: 1

N. J. A. Sloane

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.
Index entries for sequences related to f.c.c. lattice
Index entries for sequences related to specific heat

Cf. A002169 (cubic), A002167 (b.c.c.); A002166 (susceptibility).

Better description from Steven Finch
a(10) corrected, a(11)-a(12) added from Oitmaa and Bornilla by Andrey Zabolotskiy, Oct 20 2021
a(13) from Gonzalez et al. added by Andrey Zabolotskiy, May 06 2023

A002168 High-temperature series for spin-1/2 Heisenberg susceptibility on b.c.c. lattice.

Original entry on oeis.org

1, 8, 96, 1664, 36800, 1008768, 32626560, 1221399040, 51734584320, 2459086364672, 129082499311616, 7432690738003968, 464885622793134080, 31456185663820136448, 2284815238218471260160, 177611252880786297913344

Offset: 0

N. J. A. Sloane

Jaan Oitmaa, Chris Hamer and Weihong Zheng, Series expansion methods for strongly interacting lattice models, Cambridge University Press, 2006. See Table 7.8.
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 VI; b_n = a(n)*(-1)^n/2.
Index entries for sequences related to b.c.c. lattice

Cf. A002167 (specific heat, or free energy).

a(0) and a(11)-a(14) from Oitmaa et al. added by Andrey Zabolotskiy, Oct 18 2021

Name clarified, a(15) from Gonzalez et al. added by Andrey Zabolotskiy, May 10 2023

A002917 High temperature series for spin-1/2 Ising specific heat on 3-dimensional b.c.c. lattice.

Original entry on oeis.org

4, 140, 4056, 129360, 4381848, 153700408, 5519859080, 201714989064

Offset: 0

N. J. A. Sloane

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, Further application of the Padé approximant method to the Ising and Heisenberg models, Phys. Rev. 129 (1963) 99-102.
Index entries for sequences related to b.c.c. lattice
Index entries for sequences related to specific heat

Cf. A002916 (cubic), A002918 (f.c.c.), A001406 (partition function), A047711 (internal energy), A002914 (susceptibility), A002167 (Heisenberg model).

Sum_{n>=0} a(n) * v^(2*n) = (v^2-1) * (-q/2*f(v)^2 - (v^2-1) * f'(v)^2 + f(v) * (2*v*f'(v) + (v^2-1)*f''(v))) / f(v)^2, where f(v) = Sum_{n>=0} A001406(n) * v^(2*n) and q = 8 is the number of nearest neighbors. - Andrey Zabolotskiy, Feb 15 2022

Better description from Steven Finch

a(5)-a(7) from Andrey Zabolotskiy, Feb 15 2022

A002922 Specific heat for diamond.

Original entry on oeis.org

0, 6, -12, -156, 1680, 21264, -592032, -5349216, 381679872, 1095380736, -384803443200, 2445989918208, 547003852781568

Offset: 1

N. J. A. Sloane

a(n)/(n!*(-4)^n) must be equal to a_n given in Table 2 of the Oitmaa's paper. Domb & Wood's a(1)-a(7) satisfy this relation, a(8) = -5712096 and a(9) = 390388992 do not. The terms in the Data section are unambiguously retrieved from a_n. The next term a(14) is approximately -10793475537844224. The last given digit of a_8 is probably a typo. - Andrey Zabolotskiy, Jun 18 2022

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).

C. Domb and D. Wood, On high-temperature expansions for the Heisenberg model, Proc. Physical Soc., 86 (1965), 1-16.
J. Oitmaa, Diamond lattice Heisenberg antiferromagnet, J. Phys.: Condens. Matter, 30 (2018), 155801.
Index entries for sequences related to specific heat

Cf. A002923, A002165, A002167, A002169.

a(8)-a(9) corrected, a(10)-a(13) added by Andrey Zabolotskiy, Jun 18 2022 using Oitmaa's data

cp's OEIS Frontend

A002169 High temperature series for spin-1/2 Heisenberg specific heat on 3-dimensional simple cubic lattice.

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A002165 High temperature series for spin-1/2 Heisenberg specific heat on 3-dimensional f.c.c. lattice.

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A002168 High-temperature series for spin-1/2 Heisenberg susceptibility on b.c.c. lattice.

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A002917 High temperature series for spin-1/2 Ising specific heat on 3-dimensional b.c.c. lattice.

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A002922 Specific heat for diamond.

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