Yang-Lee zeros of the two- and three-state Potts model defined on [Formula presented] Feynman diagrams

We present both analytical and numerical results on the position of partition function zeros on the complex magnetic field plane of the [Formula presented] state (Ising) and the [Formula presented] state Potts model defined on [Formula presented] Feynman diagrams (thin random graphs). Our analytic results are based on the ideas of destructive interference of coexisting phases and low temperature expansions. For the case of the Ising model, an argument based on a symmetry of the saddle point equations leads us to a nonperturbative proof that the Yang-Lee zeros are located on the unit circle, although no circle theorem is known in this case of random graphs. For the [Formula presented] state Potts model, our perturbative results indicate that the Yang-Lee zeros lie outside the unit circle. Both analytic results are confirmed by finite lattice numerical calculations. © 2003 The American Physical Society.