# Zeros of the Potts Model Partition Function in the Large-$q$ Limit

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We study the zeros of the $q$-state Potts model partition function $Z\Lambda,q,v$ for large $q$, where $v$ is the temperature variable and $\Lambda$ is a section of a regular $d$-dimensional lattice with coordination number $\kappa \Lambda$ and various boundary conditions. We consider the simultaneous thermodynamic limit and $q \to \infty$ limit and show that when these limits are taken appropriately, the zeros lie on the unit circle $|x \Lambda|=1$ in the complex $x \Lambda$ plane, where $x \Lambda=v q^{-2-\kappa \Lambda}$. For large finite sections of some lattices we also determine the circular loci near which the zeros lie for large $q$.

Autor: Shu-Chiuan Chang; Robert Shrock

Fuente: https://archive.org/