Thin Fisher zeros

Various authors have suggested that the loci of partition function zeros can profitably be regarded as phase boundaries in the complex temperature or field planes. We obtain the Fisher zeros for Ising and Potts models on non-planar (`thin') regular random graphs using this approach, and note that the locus of Fisher zeros on a Bethe lattice is identical to the corresponding random graph. Since the number of states q appears as a parameter in the Potts solution the limiting locus of chromatic zeros is also accessible.