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

TL;DR

This paper investigates the complex-temperature zeros of the Potts model's partition function on honeycomb and kagomé lattices, revealing insights into phase diagrams and showing no phase transition for certain antiferromagnetic cases.

Contribution

It provides new calculations of CT zeros for the Potts model on these lattices, comparing boundary conditions and analyzing CT singularities.

Findings

No phase transition for q=4 and q=5 antiferromagnets on kagomé lattice

Comparison of boundary conditions affects CT zero distributions

Insights into CT phase diagrams and singularities

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.