A002978 Low-temperature series in y = exp(2J/kT) for antiferromagnetic susceptibility for the Ising model on honeycomb structure. (Formerly M3189)

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

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