A003196 -id:A003196 - cp's OEIS frontend

A002924 Ferromagnetic susceptibility series for f.c.c. lattice.

0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 24, -26, 0, 0, 72, 378, -1080, 665, 384, 1968, 2016, -25698, 39552, -3872, 20880, -65727, -379072, 1277646, -986856, 176978, -2163504, -1818996, 27871080, -47138844, 20789424, -36509652, 77055330, 393046656, -1402934816, 1403843388

Offset: 0

N. J. A. Sloane

sign

C. Domb, Ising model, in Phase Transitions and Critical Phenomena, vol. 3, ed. C. Domb and M. S. Green, Academic Press, 1974; p. 421.
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, Ising model, Phase Transitions and Critical Phenomena 3 (1974), 257, 380-381, 384-387, 390-391, 412-423. (Annotated scanned copy)
J. W. Essam and M. E. Fisher, Padé approximant studies of the lattice gas and Ising ferromagnet below the critical point, J. Chem. Phys., 38 (1963), 802-812.
M. F. Sykes et al., Derivation of low-temperature expansions for Ising model VI. Three-dimensional lattices - temperature grouping, J. Phys. A 6 (1973), 1507-1516.
Index entries for sequences related to f.c.c. lattice

Cf. A002926 (cubic), A002925 (b.c.c.), A002892 (partition function), A003196 (magnetization), A002921 (high-temperature).

a(35)-a(40) from Sykes et al. added by Andrey Zabolotskiy, Feb 16 2022

A002928 Magnetization for square lattice.

Original entry on oeis.org

1, 0, -2, -8, -34, -152, -714, -3472, -17318, -88048, -454378, -2373048, -12515634, -66551016, -356345666, -1919453984, -10392792766, -56527200992, -308691183938, -1691769619240, -9301374102034

Offset: 0

N. J. A. Sloane, Simon Plouffe

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).
J. M. Yeomans, Statistical mechanics of phase transitions, Oxford Univ. Press, 1992, p. 93.

C. Domb, Ising model, Phase Transitions and Critical Phenomena 3 (1974), 257, 380-381, 384-387, 390-391, 412-423. (Annotated scanned copy)
David Park, A summation method for crystal statistics, Physica 22 (1956), 932-940.

Cf. other structures: A007206, A007207, A002929, A002930, A003193, A003196.
Cf. higher spins: A010102, A010105/A030120, A010103, A010106/A030121, A010104.
Cf. Potts model: A057374, A057378.
Cf. A002927 (susceptibility).

series((1+x)^(1/4)*(1-6*x+x^2)^(1/8)/(1-x)^(1/2),x,40).

CoefficientList[Series[(1+x)^(1/4)*(1-6*x+x^2)^(1/8)/(1-x)^(1/2), {x, 0, 20}], x] (* Vaclav Kotesovec, Apr 27 2024 *)

n*a(n) + 6*(-n+1)*a(n-1) + 4*a(n-2) + 6*(n-3)*a(n-3) + (-n+4)*a(n-4) = 0. - R. J. Mathar, Mar 08 2013

a(n) ~ -Gamma(1/8) * (1 + sqrt(2))^(2*n - 1/2) / (Pi * 2^(57/16) * n^(9/8)). - Vaclav Kotesovec, Apr 27 2024

A002892 Low-temperature series for partition function for spin-1/2 Ising model on f.c.c. lattice.

Original entry on oeis.org

1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 6, -6, 0, 0, 8, 42, -114, 66, 24, 123, 134, -1563, 2262, -405, 846, -2532, -15182, 47961, -37992, 8044, -59694, -57117, 742394, -1233840, 597456, -798392, 1447162, 7898736, -27134598, 27649335

Offset: 0

N. J. A. Sloane

sign

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, On the theory of cooperative phenomena in crystals, Advances in Phys., 9 (1960), 149-361: part 1, part 2.
C. Domb and A. J. Guttmann, Low-temperature series for the Ising model, J. Phys. C: Solid State Phys., 3 (1970), 1652-1660.
M. F. Sykes, D. S. Gaunt, J. W. Essam and C. J. Elliott, Derivation of low-temperature expansions for Ising model. VI. Three-dimensional lattices-temperature grouping, J. Phys. A: Math. Nucl. Gen., 6 (1973), 1507-1516.
Index entries for sequences related to f.c.c. lattice

Cf. A001407 (high-temperature), A002891 (cubic lattice), A002924 (susceptibility), A003196 (magnetization).

Name clarified, missing minus signs added to a(12) and a(17), and terms a(22) and beyond added by Andrey Zabolotskiy, Feb 14 2022

A003193 Magnetization for body-centered cubic lattice.

Original entry on oeis.org

1, 0, 0, 0, -2, 0, 0, -16, 18, 0, -168, 384, -314, -1632, 6264, -9744, -10014, 86976, -205344, 80176, 1009338, -3579568, 4575296, 8301024, -54012882, 112640896, -5164464, -694845120, 2160781086

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. 421.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

C. Domb, Ising model, Phase Transitions and Critical Phenomena 3 (1974), 257, 380-381, 384-387, 390-391, 412-423. (Annotated scanned copy)
M. F. Sykes, J. W. Essam and D. S. Gaunt, Derivation of low-temperature expansions for the Ising model of a ferromagnet and an antiferromagnet, J. Math. Phys. 6 (1965), 283-298.
M. F. Sykes, D. S. Gaunt, J. W. Essam and C. J. Elliott, Derivation of low-temperature expansions for Ising model. VI. Three-dimensional lattices-temperature grouping, J. Phys. A: Math. Nucl. Gen., 6 (1973), 1507-1516.
Index entries for sequences related to b.c.c. lattice

Cf. A002929 (cubic), A003196 (f.c.c.), A002925 (ferromagnetic susceptibility), A003194 (antiferromagnetic susceptibility).

a(27)-a(28) from Sykes et al. (1973) added by Andrey Zabolotskiy, Feb 16 2022

cp's OEIS Frontend

A002924 Ferromagnetic susceptibility series for f.c.c. lattice.

Views

Author

Keywords

References

Links

Crossrefs

Extensions

A002928 Magnetization for square lattice.

Views

Author

Keywords

References

Links

Crossrefs

Programs

Maple

Mathematica

Formula

A002892 Low-temperature series for partition function for spin-1/2 Ising model on f.c.c. lattice.

Views

Author

Keywords

References

Links

Crossrefs

Extensions

A003193 Magnetization for body-centered cubic lattice.

Views

Author

Keywords

References

Links

Crossrefs

Extensions