A003193 -id:A003193 - cp's OEIS frontend

A002928 Magnetization for square lattice.

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

A003196 Magnetization series for face-centered cubic lattice.

Original entry on oeis.org

1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, -24, 26, 0, 0, -48, -252, 720, -438, -192, -984, -1008, 12924, -19536, 3062, -8280, 26694, 153536, -507948, 406056, -79532, 729912, 631608, -9279376, 15771600, -7467336, 10935114, -21835524, -112752684, 400576168, -410287368

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. [has a typo in a(35)]
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 et al., Derivation of low-temperature expansions for Ising model VI. Three-dimensional lattices - temperature grouping, J. Phys. A 6 (1973), 1507-1516.

Cf. A003193.

A371049 Low temperature series for spin-1/2 Ising partition function on body-centered cubic lattice.

Original entry on oeis.org

1, 0, 0, 0, 1, 0, 0, 4, -4, 0, 28, -60, 44, 204, -750, 1084, 979, -8444, 18886, -7568, -82269, 280288, -348172, -576712, 3677331, -7445964, 569558, 41740944, -126624684

Offset: 1

Andrey Zabolotskiy, Mar 11 2024

The series is in the variable u = exp(-4J/kT).

The expansion of the logarithm of the g.f. of this sequence is given in Domb & Guttmann's Table 1 (with a reference to Sykes et al., 1965) and continued in Eq. (4.14) of Sykes et al., 1973.

Claude Itzykson and Jean-Michel Drouffe, Statistical field theory, vol. 2, Cambridge University Press, 1989. Eq. (120) is supposed to give the logarithm of the g.f., but its second half is erroneously switched with the second half of Eq. (121). These second halves are Eqs. (4.15) and (4.14) of Sykes et al., 1973.

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, 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. A002891 (simple cubic), A002892 (f.c.c.); A003193 (magnetization), A002925 (ferromagnetic susceptibility), A007218 (antiferromagnetic susceptibility); A001406 (high temperature).

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A002928 Magnetization for square lattice.

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A003196 Magnetization series for face-centered cubic lattice.

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A371049 Low temperature series for spin-1/2 Ising partition function on body-centered cubic lattice.

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