A010115 -id:A010115 - cp's OEIS frontend

A002927 Low temperature series for spin-1/2 Ising magnetic susceptibility on 2D square lattice.

0, 0, 1, 8, 60, 416, 2791, 18296, 118016, 752008, 4746341, 29727472, 185016612, 1145415208, 7059265827, 43338407712, 265168691392, 1617656173824, 9842665771649, 59748291677832, 361933688520940, 2188328005246304, 13208464812265559, 79600379336505560, 479025509574159232

Offset: 0

N. J. A. Sloane, Simon Plouffe

nonn

The zero-field susceptibility per spin is 4m^2/kT * Sum_{n >= 0} a(n) * u^n, where u = exp(-4J/kT). (m is the magnetic moment of a single spin; this factor may be present or absent depending on the precise definition of the susceptibility.) The b-file has been obtained from the series by Guttmann and Jensen via the substitution r = u/(1-u)^2 and dividing by 4. - Andrey Zabolotskiy, Feb 11 2022

C. Domb, Ising model, in Phase Transitions and Critical Phenomena, vol. 3, ed. C. Domb and M. S. Green, Academic Press, 1974; p. 421.
S. R. Finch, Mathematical Constants, Cambridge, 2003, pp. 391-406.
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).

Andrey Zabolotskiy, Table of n, a(n) for n = 0..1305
R. J. Baxter and I. G. Enting, Series expansions for corner transfer matrices: the square lattice Ising model, J. Stat. Physics 21 (1979) 103-123.
C. Domb, Ising model, Phase Transitions and Critical Phenomena 3 (1974), 257, 380-381, 384-387, 390-391, 412-423. (Annotated scanned copy)
I. G. Enting, A, J. Guttmann and I. Jensen, Low-Temperature Series Expansions for the Spin-1 Ising Model, arXiv:hep-lat/9410005, 1994; J. Phys. A. 27 (1994) 6987-7005.
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.
Steven R. Finch, Lenz-Ising Constants [broken link]
Steven R. Finch, Lenz-Ising Constants [From the Wayback Machine]
Tony Guttmann, Homepage. See Numerical Data, Ising square lattice susceptibility series, Low temperature series.
Iwan Jensen, Series for the Ising model

Cf. A002906 (high-temperature), A002979 (antiferromagnetic susceptibility), A029872 (specific heat), A002928 (magnetization), A002890 (partition function), A047709 (hexagonal lattice), A002912 (honeycomb), A002926 (cubic lattice), A010115 (spin-1 Ising).

a(n) ~ c * n^(3/4) * (1 + sqrt(2))^(2*n), where c = 0.0187325517235678... - Vaclav Kotesovec, May 06 2024

Corrections and updates from Steven Finch

a(0) = a(1) = 0 prepended, terms a(20) and beyond added by Andrey Zabolotskiy, Feb 10 2022

A010102 Spontaneous magnetization coefficients for square lattice spin 1 Ising model.

Original entry on oeis.org

1, 0, 0, 0, -1, 0, 0, -4, 3, 0, -30, 48, -52, -120, 368, -612, -254, 2524, -6216, 4040, 11805, -49400, 68268, 14928, -332511, 734508, -568038, -1641320, 6202774, -9239676, -2503162, 42749908, -99021392, 72255812, 215763902

Offset: 0

N. J. A. Sloane, Simon Plouffe

sign

I. Jensen, Table of n, a(n) for n = 0..113 (from link below)
I. G. Enting, A, J. Guttmann and I. Jensen, Low-Temperature Series Expansions for the Spin-1 Ising Model, arXiv:hep-lat/9410005, 1994; J. Phys. A. 27 (1994) 6987-7006.
I. Jensen, More terms
Iwan Jensen and Anthony J. Guttmann, Series expansions of the percolation probability for directed square and honeycomb lattices, arXiv:cond-mat/9509121, 1995; J. Phys. A 28 (1995), no. 17, 4813-4833.

Cf. A002928, A010103, A010104, A010105, A010106, A010107, A010111, A010115.

Link corrected by Ralf Stephan, Aug 04 2013

A010107 Partition function coefficients for square lattice spin 1 Ising model.

Original entry on oeis.org

1, 0, 0, 0, 1, 0, 0, 2, -1, 0, 10, -14, 13, 30, -85, 124, 50, -476, 1047, -642, -1949, 7220, -9547, -2690, 42625, -90224, 62414, 190074, -683506, 952260, 290296, -4276192, 9356547, -6406858, -20006212, 73731040, -103077077

Offset: 0

N. J. A. Sloane, Simon Plouffe

sign

I. Jensen, Table of n, a(n) for n = 0..113 (from link below)
I. G. Enting, A, J. Guttmann and I. Jensen, Low-Temperature Series Expansions for the Spin-1 Ising Model, arXiv:hep-lat/9410005, 1994; J. Phys. A. 27 (1994) 6987-7006.
I. Jensen, More terms
Iwan Jensen, Anthony J. Guttmann, Series expansions of the percolation probability for directed square and honeycomb lattices, arXiv:cond-mat/9509121, 1995; J. Phys. A 28 (1995), no. 17, 4813-4833.

Cf. A010102, A010115, A010111.

Cf. A010108, A010109, A010110, A056620.

"Free energy" corrected to "partition function" (basically the exponential of the free energy) in the name by Andrey Zabolotskiy, Feb 11 2022

cp's OEIS Frontend

A002927 Low temperature series for spin-1/2 Ising magnetic susceptibility on 2D square lattice.

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A010102 Spontaneous magnetization coefficients for square lattice spin 1 Ising model.

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A010107 Partition function coefficients for square lattice spin 1 Ising model.

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