A002164 E.g.f.: high-temperature series in J/2kT for logarithm of partition function for the spin-1/2 linear (1D) Heisenberg model. (Formerly M2601 N1028)

0, 3, -6, -30, 360, 504, -44016, 204048, 8261760, -128422272, -1816480512, 76562054400, 124207469568, -51042832542720, 580686719698944, 36632422458820608, -1141184282933624832, -23612862502431719424, 1881307594631033978880, 253019693533000826880

Offset

1,2

Comments

From Andrey Zabolotskiy, Feb 24 2022: (Start)

The power-series parameter may be also written as J/4kT, depending on the particular form of the Hamiltonian.

a(n) = alpha_n / (n * (n-1)), where alpha_n are given in Table I of Shiroishi & Takahashi. (End)

References

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 = 1..51

G. A. Baker et al., High-temperature series expansions for the spin-1/2 Heisenberg model by the method of irreducible representations of the symmetric group, Phys. Rev., 135 (1964), pages A_1272-A_1277.

Masahiro Shiroishi and Minoru Takahashi, Integral Equation Generates High-Temperature Expansion of the Heisenberg Chain, Phys. Rev. Lett., 89 (2002), 117201.

Crossrefs

Cf. A005399.

Sequence in context: A061137 A012280 A282132 * A331661 A117805 A154135

Adjacent sequences: A002161 A002162 A002163 * A002165 A002166 A002167

Keyword

sign

Author

N. J. A. Sloane

Extensions

Name clarified, terms a(14) and beyond added by Andrey Zabolotskiy, Feb 24 2022

Status

approved