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A002906 High temperature series for spin-1/2 Ising magnetic susceptibility on 2D square lattice.
(Formerly M3447 N1401)
12
1, 4, 12, 36, 100, 276, 740, 1972, 5172, 13492, 34876, 89764, 229628, 585508, 1486308, 3763460, 9497380, 23918708, 60080156, 150660388, 377009364, 942106116, 2350157268, 5855734740, 14569318492, 36212402548, 89896870204 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
The zero-field susceptibility per spin is m^2/kT * Sum_{n >= 0} a(n) * v^n, where v = tanh(J/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 t = v/(1-v^2). - Andrey Zabolotskiy, Feb 11 2022
REFERENCES
C. Domb, Ising model, in Phase Transitions and Critical Phenomena, vol. 3, ed. C. Domb and M. S. Green, Academic Press, 1974; p. 380.
S. R. Finch, Mathematical Constants, Cambridge, 2003, pp. 391-406.
A. J. Guttmann, Asymptotic analysis of power-series expansions, pp. 1-234 of C. Domb and J. L. Lebowitz, editors, Phase Transitions and Critical Phenomena. Vol. 13, Academic Press, NY, 1989.
B. G. Nickel, personal communication.
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).
LINKS
Andrey Zabolotskiy, Table of n, a(n) for n = 0..2043 (terms up to n = 116 from Fred Hucht)
C. Domb, Ising model, Phase Transitions and Critical Phenomena 3 (1974), 257, 380-381, 384-387, 390-391, 412-423. (Annotated scanned copy)
Steven R. Finch, Lenz-Ising Constants [broken link]
Steven R. Finch, Lenz-Ising Constants [From the Wayback Machine]
M. E. Fisher and R. J. Burford, Theory of critical point scattering and correlations I: the Ising model, Phys. Rev. 156 (1967), 583-621.
S. Gartenhaus and W. S. McCullough, Higher order corrections for the quadratic Ising lattice susceptibility at criticality, Phys. Rev. B 38 (1988) 11688-11703.
A. J. Guttmann, Asymptotic analysis of power-series expansions, pp. 1-13, 56-57, 142-143, 150-151 from of C. Domb and J. L. Lebowitz, editors, Phase Transitions and Critical Phenomena. Vol. 13, Academic Press, NY, 1989. (Annotated scanned copy)
Tony Guttmann, Homepage. See Numerical Data, Ising square lattice susceptibility series, High temperature series.
B. Nickel, On the singularity structure of the 2D Ising model susceptibility, Journal of Physics A, Math. Gen. 32, 3889 (1999); Addendum, 33, 1693 (2000).
M. F. Sykes, D. G. Gaunt, P. D. Roberts and J. A. Wyles, High temperature series for the susceptibility of the Ising model, I. Two dimensional lattices, J. Phys. A 5 (1972) 624-639.
M. F. Sykes et al., The asymptotic behavior of selfavoiding walks and returns on a lattice, J. Phys. A 5 (1972), 653-660.
CROSSREFS
Cf. A002927 (low-temperature), A002908 (energy), A002920 (hexagonal lattice), A002910 (honeycomb), A002913 (cubic lattice), A005401 (Heisenberg).
Sequence in context: A051041 A192626 A294782 * A191756 A001411 A095350
KEYWORD
nonn,nice
AUTHOR
EXTENSIONS
Corrections and updates from Steven Finch
More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Mar 01 2008
STATUS
approved

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Last modified March 29 02:23 EDT 2024. Contains 371264 sequences. (Running on oeis4.)