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A002978 Low-temperature series in y = exp(2J/kT) for antiferromagnetic susceptibility for the Ising model on honeycomb structure.
(Formerly M3189)
3
0, 0, 4, 0, 12, 8, 48, 96, 320, 888, 2748, 8384, 26340, 83568, 268864, 873648, 2865216, 9470784, 31525524, 105594912, 355673804, 1204059144, 4094727168, 13983145888, 47932777680, 164881688088, 568990371212, 1969356192624, 6834965581764, 23782468159920 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Previous name was: Susceptibility series for honeycomb.

REFERENCES

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Table of n, a(n) for n=1..30.

Y. Chan, A. J. Guttmann, B. G. Nickel, J. H. H. Perk, The Ising Susceptibility Scaling Function, J Stat Phys 145 (2011), 549-590; arXiv:1012.5272 [cond-mat.stat-mech], 2010-2020. Gives 641 term in the file Honeycomb_y641_af_.txt.

M. F. Sykes and M. E. Fisher, Antiferromagnetic susceptibility of the plane square and honeycomb Ising lattices, Physica, 28 (1962), 919-938.

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.

FORMULA

From Andrey Zabolotskiy, Mar 03 2021: (Start)

a(n) = 4*A007214(n-3).

G.f.: 8*t(u(y)) - 4*h(y), where t(u) is the g.f. of A047709, h(y) is the g.f. of A002912, and u(y) = y/(1-y+y^2) [Sykes & Fisher, p. 934-935]. (End)

CROSSREFS

Cf. A002910, A002912, A007214-A007218, A057391, A057395, A047709, A128834.

Sequence in context: A273329 A141554 A076600 * A273609 A273505 A273706

Adjacent sequences:  A002975 A002976 A002977 * A002979 A002980 A002981

KEYWORD

nonn,nice

AUTHOR

N. J. A. Sloane

EXTENSIONS

New name from and more terms from Chan et al added by Andrey Zabolotskiy, Mar 03 2021

STATUS

approved

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Last modified April 15 06:12 EDT 2021. Contains 342975 sequences. (Running on oeis4.)