Narrow Results

We calculate zeros of the q-state Potts model partition function Z(G_Λ,q,v) for large q, where v is the temperature variable and G_Λ is a section of a lattice Λ with coordination number κ_Λ and various boundary conditions. Lattice types studied include square, triangular, honeycomb, and kagomé. We show that for large q these zeros take on approximately circular patterns in the complex x_Λ plane, where x_Λ=v/q^2/κ_Λ. This generalizes a known result for the square lattice to the other lattices considered.