OFFSET
0,4
COMMENTS
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
REFERENCES
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).
LINKS
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
FORMULA
a(n) ~ c * n^(3/4) * (1 + sqrt(2))^(2*n), where c = 0.0187325517235678... - Vaclav Kotesovec, May 06 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
Corrections and updates from Steven Finch
a(0) = a(1) = 0 prepended, terms a(20) and beyond added by Andrey Zabolotskiy, Feb 10 2022
STATUS
approved