Die Polynome von Yang-Lee und ihre Nullstellen (with H. Carnal). Elemente der Mathematik, 45, 130-137 (1990)
(The polynomials of Yang-Lee and their zeroes)

The free energy of the Ising model on a finite graph, having one spin in { +1,-1 } assigned to each of the n vertices, is defined by $ -\lim _{{n -> \infty}} (kT/n) \log \sum \exp {-E/(kT)} $, where E denotes the energy of the system and k and T are some constants. An accumulation of zeroes of the partition function indicates a phase transition of the system. We show for the Ising model without external field that, for nonpositive interactions, these zeroes always lie on the unit circle, whereas for nonnegative interactions, they lie on the negative real half-axis, on the unit circle, or on the union of both sets for the complete and cyclic graph. In contrast, for the regular trees of degree at least 3, of the order square root n of these n zeroes are located away from the negative real half-axis and the unit circle. Recursions of generating functions make important ingredients.