A002165 -id:A002165 - 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

A002167 High temperature series for spin-1/2 Heisenberg specific heat on 3-dimensional b.c.c. lattice.

Original entry on oeis.org

0, 12, -24, 168, 1440, 24480, -297024, 28017216, -533681664, 41156316672, -503287538688, 53001415916544, -1839416689004544, 246102905022713856, -9001661201883684864

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

Cf. A002169 (cubic), A002165 (f.c.c.); A002168 (susceptibility).

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

A002918 High temperature series for spin-1/2 Ising specific heat on 3-dimensional f.c.c. lattice.

Original entry on oeis.org

6, 48, 390, 3216, 26844, 229584, 2006736, 17809008, 159799812, 1446245424, 13181330772, 120849559824, 1113598633188

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.
A. J. Guttmann and G. S. Joyce, Critical behaviour of an isotropic spin system, J. Phys. C: Solid State Phys., 6 (1973), 2691-2712. See Table 1.
Index entries for sequences related to f.c.c. lattice
Index entries for sequences related to specific heat

Cf. A002916 (cubic), A002917 (b.c.c.), A002921 (susceptibility), A001407 (partition function), A002165 (Heisenberg).

G.f.: (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) is the g.f. of A001407 and q = 12 is the number of nearest neighbors. - Andrey Zabolotskiy, Feb 15 2022

Better description from Steven Finch
a(8)-a(10) from Guttmann & Joyce added by Andrey Zabolotskiy, Feb 02 2022
a(11)-a(12) from Andrey Zabolotskiy, Feb 15 2022

A002921 Susceptibility series for f.c.c. lattice.

Original entry on oeis.org

1, 12, 132, 1404, 14652, 151116, 1546332, 15734460, 159425580, 1609987708, 16215457188, 162961837500, 1634743178420, 16373484437340, 163778159931180, 1636328839130860

Offset: 0

N. J. A. Sloane

C. Domb, Ising model, in Phase Transitions and Critical Phenomena, vol. 3, ed. C. Domb and M. S. Green, Academic Press, 1974; p. 381.
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, Self-avoiding walks and the Ising and Heisenberg models, Solid State Physics = Journal of Physics C, 3 (1970) 256-284.
C. Domb, Ising model, Phase Transitions and Critical Phenomena 3 (1974), 257, 380-381, 384-387, 390-391, 412-423. (Annotated scanned copy)
M. E. Fisher and R. J. Burford, Theory of critical point scattering and correlations I: the Ising model, Phys. Rev. 156 (1967), 583-621.
D. S. Gaunt, High Temperature Series Analysis for the Three-Dimensional Ising Model: A Review of Some Recent Work, in: Phase Transitions: Cargèse 1980, eds. Maurice Lévy, Jean-Claude Le Guillou and Jean Zinn-Justin, Springer, Boston, MA, 1982.
Sati McKenzie, High-temperature reduced susceptibility of the Ising model, J. Phys. A: Math. Gen., 8 (1975), L102-L105.
N. J. A. Sloane, "A Handbook of Integer Sequences" Fifty Years Later, arXiv:2301.03149 [math.NT], 2023, p. 5.
M. F. Sykes, D. G. Gaunt, P. D. Roberts and J. A. Wyles, High temperature series for the susceptibility of the Ising model, II. Three dimensional lattices, J. Phys. A 5 (1972) 640-652.
Index entries for sequences related to f.c.c. lattice

Cf. A002913 (cubic), A002914 (b.c.c.); A002918 (specific heat).

Cf. Heisenberg model: A002166; A002170 (cubic), A002168 (b.c.c.); A002165 (specific heat).

a(13)-a(15) from McKenzie added by Andrey Zabolotskiy, Feb 05 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.

Views

Author

Keywords

References

Links

Crossrefs

Extensions

A002167 High temperature series for spin-1/2 Heisenberg specific heat on 3-dimensional b.c.c. lattice.

Views

Author

Keywords

References

Links

Crossrefs

Extensions

A002918 High temperature series for spin-1/2 Ising specific heat on 3-dimensional f.c.c. lattice.

Views

Author

Keywords

References

Links

Crossrefs

Formula

Extensions

A002921 Susceptibility series for f.c.c. lattice.

Views

Author

Keywords

References

Links

Crossrefs

Extensions

A002922 Specific heat for diamond.

Views

Author

Keywords

Comments

References

Links

Crossrefs

Extensions