%I M3447 N1401 #57 May 04 2024 05:13:01
%S 1,4,12,36,100,276,740,1972,5172,13492,34876,89764,229628,585508,
%T 1486308,3763460,9497380,23918708,60080156,150660388,377009364,
%U 942106116,2350157268,5855734740,14569318492,36212402548,89896870204
%N High temperature series for spin-1/2 Ising magnetic susceptibility on 2D square lattice.
%C 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
%D C. Domb, Ising model, in Phase Transitions and Critical Phenomena, vol. 3, ed. C. Domb and M. S. Green, Academic Press, 1974; p. 380.
%D S. R. Finch, Mathematical Constants, Cambridge, 2003, pp. 391-406.
%D 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.
%D B. G. Nickel, personal communication.
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Andrey Zabolotskiy, <a href="/A002906/b002906.txt">Table of n, a(n) for n = 0..2043</a> (terms up to n = 116 from Fred Hucht)
%H C. Domb, <a href="/A007239/a007239.pdf">Ising model</a>, Phase Transitions and Critical Phenomena 3 (1974), 257, 380-381, 384-387, 390-391, 412-423. (Annotated scanned copy)
%H Steven R. Finch, <a href="http://www.people.fas.harvard.edu/~sfinch/constant/ising/ising.html">Lenz-Ising Constants</a> [broken link]
%H Steven R. Finch, <a href="http://web.archive.org/web/20010207201511/http://www.mathsoft.com:80/asolve/constant/ising/ising.html">Lenz-Ising Constants</a> [From the Wayback Machine]
%H M. E. Fisher and R. J. Burford, <a href="https://doi.org/10.1103/PhysRev.156.583">Theory of critical point scattering and correlations I: the Ising model</a>, Phys. Rev. 156 (1967), 583-621.
%H S. Gartenhaus and W. S. McCullough, <a href="https://doi.org/10.1103/PhysRevB.38.11688">Higher order corrections for the quadratic Ising lattice susceptibility at criticality</a>, Phys. Rev. B 38 (1988) 11688-11703.
%H A. J. Guttmann, <a href="/A002906/a002906.pdf">Asymptotic analysis of power-series expansions</a>, 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)
%H Tony Guttmann, <a href="https://web.archive.org/web/20090705023809 /http://www.ms.unimelb.edu.au/~tonyg/">Homepage</a>. See Numerical Data, Ising square lattice susceptibility series, High temperature series.
%H Iwan Jensen, <a href="https://web.archive.org/web/20090705035447if_ /http://www.ms.unimelb.edu.au/~iwan/ising/Ising_ser.html">Series for the Ising model</a>
%H B. Nickel, <a href="https://doi.org/10.1088/0305-4470/32/21/303">On the singularity structure of the 2D Ising model susceptibility</a>, Journal of Physics A, Math. Gen. 32, 3889 (1999); <a href="https://doi.org/10.1088/0305-4470/33/8/313">Addendum</a>, 33, 1693 (2000).
%H M. F. Sykes, <a href="http://dx.doi.org/10.1063/1.1724212">Some counting theorems in the theory of the Ising problem and the excluded volume problem</a>, J. Math. Phys., 2 (1961), 52-62.
%H M. F. Sykes, D. G. Gaunt, P. D. Roberts and J. A. Wyles, <a href="https://doi.org/10.1088/0305-4470/5/5/004">High temperature series for the susceptibility of the Ising model, I. Two dimensional lattices</a>, J. Phys. A 5 (1972) 624-639.
%H M. F. Sykes et al., <a href="http://dx.doi.org/10.1088/0305-4470/5/5/007">The asymptotic behavior of selfavoiding walks and returns on a lattice</a>, J. Phys. A 5 (1972), 653-660.
%H Peter Young, <a href="https://web.archive.org/web/20150912072903 /http://www.apyoung.com/~peter/219/series.dat">Coefficients in the series expansions</a>
%F a(n) ~ c * n^(3/4) * (1 + sqrt(2))^n, where c = 0.839697019... - _Vaclav Kotesovec_, May 04 2024
%Y Cf. A002927 (low-temperature), A002908 (energy), A002920 (hexagonal lattice), A002910 (honeycomb), A002913 (cubic lattice), A005401 (Heisenberg).
%K nonn,nice
%O 0,2
%A _N. J. A. Sloane_
%E Corrections and updates from _Steven Finch_
%E More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Mar 01 2008