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A002906 High temperature series for spin-1/2 Ising magnetic susceptibility on 2D square lattice.
(Formerly M3447 N1401)
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)



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.

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. 1-234 of C. Domb and J. L. Lebowitz, editors, Phase Transitions and Critical Phenomena. Vol. 13, Academic Press, NY, 1989.

B. G. Nickel, personal communication.

B. Nickel, Journal of Physics A, Math. Gen. 32, 3889 (1999), 33, 1693 (2000)

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).

M. F. Sykes, Some counting theorems in the theory of the Ising problem and the excluded volume problem, J. Math. Phys., 2 (1961), 52-62.

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.


Fred Hucht (fred(AT)thp.uni-due.de), Oct 2008, Table of n, a(n) for n=0..116 [Coefficients of chi = Sum[a[n] z^n,{n,0,116}] with z=Tanh[1/kBT]]

S. R. Finch, Lenz-Ising Constants

Peter Young, Coefficients in the series expansions


Sequence in context: A002842 A051041 A192626 * A191756 A001411 A095350

Adjacent sequences:  A002903 A002904 A002905 * A002907 A002908 A002909




N. J. A. Sloane.


Corrections and updates from Steven Finch

More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Mar 01 2008



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Last modified November 30 21:08 EST 2015. Contains 264673 sequences.