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

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

Offset: 1

Author

N. J. A. Sloane

Keywords

• sign

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.

Extensions

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