Complex-Temperature Partition Function Zeros of the Potts Model on the Honeycomb and Kagom\'e Lattices

Abstract

We calculate complex-temperature (CT) zeros of the partition function for the $q$-state Potts model on the honeycomb and kagom\'e lattices for several values of $q$. These give information on the CT phase diagrams. A comparison of results obtained for different boundary conditions and a discussion of some CT singularities are given. Among other results, our findings show that the Potts antiferromagnet with $q=4$ and $q=5$ on the kagom\'e lattice has no phase transition at either finite or zero temperature.