Zeros of the Potts Model Partition Function in the Large-$q$ Limit
Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, Genova, Italy, (9-13 July 2007)Abstract
We present the zero distributions of the $q$-state Potts model partition function $Z(Łambda,q,v)$ for large $q$, where $v$ is the temperature variable and $Łambda$ is a section of a regular two-dimensional lattice with coordination number $\kappa_Łambda$ 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 $x_Łambda$ plane, where $x_Łambda=vq^-2/\kappa_Łambda$. When the thermodynamic limit and the limit of infinite $q$ are taken appropriately, all the zeros are located on the unit circle $|x_Łambda|=1$.