Study of the Potts Model on the Honeycomb and Triangular Lattices: Low-Temperature Series and Partition Function Zeros

TL;DR

This paper investigates the low-temperature series and partition function zeros of the q-state Potts model on honeycomb and triangular lattices, revealing insights into complex-temperature phase boundaries and extending previous analyses to additional lattice and q values.

Contribution

It provides new low-temperature series data and analyzes the complex-temperature zeros for the Potts model on various lattices, expanding understanding of phase boundaries.

Findings

Locations of singularities correlate with phase boundaries.

Extended analysis to q=3 on honeycomb lattice.

Included discussion for Potts model on kagome lattice.

Abstract

We present and analyze low-temperature series and complex-temperature partition function zeros for the $q$-state Potts model with $q=4$ on the honeycomb lattice and $q=3,4$ on the triangular lattice. A discussion is given as to how the locations of the singularities obtained from the series analysis correlate with the complex-temperature phase boundary. Extending our earlier work, we include a similar discussion for the Potts model with $q=3$ on the honeycomb lattice and with $q=3,4$ on the kagom\'e lattice.