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

Abstract

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 $q$.

11 pages, revtex, 16 eps figures

References in corpus (5)

• Exact Potts Model Partition Functions on Wider Arbitrary-Length Strips of the Square Lattice
• Exact Potts Model Partition Function for Strips of the Square Lattice
• Complex-Temperature Phase Diagrams for the q-State Potts Model on Self-Dual Families of Graphs and the Nature of the $q\to \infty$ Limit
• Transfer Matrices for the Partition Function of the Potts Model on Cyclic and Mobius Lattice Strips
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Cited by in corpus (5)

• $q$-Plane Zeros of the Potts Partition Function on Diamond Hierarchical Graphs
• Zeros of the Potts Model Partition Function on Sierpinski Graphs
• Global disorder transition in the community structure of large-q Potts systems
• The stability to instability transition in the structure of large scale networks
• Potts Partition Function Zeros and Ground State Entropy on Hanoi Graphs