On the singularity structure of the 2D Ising model susceptibility. (English) Zbl 0936.82006
Summary: Some simplifications of the integrals , derived by T. T. Wu [Phys. Rev. B (3) 13, 316-374 (1976)] that contribute to the zero field susceptibility of the 2D square lattice Ising model are reported. In particular, several alternate expressions for the integrands in are determined which greatly facilitate both the generation of high-temperature series and analytical analysis. One can show that as series, where is the high-temperature variable with the conventional normalized inverse temperature. Analysis of the integrals near symmetry points of the integrands shows that is singular on the unit circle at where , , . The singularities, excepted, are logarithmic branch points of order with . There is numerical evidence from series that these van Hove points, in addition to the known points at and , exhaust the singularities on the unit circle. Barring cancellation from extra (unobserved) singularities one can conclude that is a natural boundary for the susceptibility.
|82B20||Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs|
|82B23||Exactly solvable models; Bethe ansatz|