Partition Function Zeros of a Restricted Potts Model on Lattice Strips and Effects of Boundary Conditions

TL;DR

This paper computes the exact partition function zeros of the Potts model on lattice strips with various boundary conditions, revealing how these zeros accumulate and form loci in the thermodynamic limit.

Contribution

It provides exact calculations of the partition function zeros for the Potts model on different lattice strips, analyzing the effects of boundary conditions on the zeros' accumulation loci.

Findings

Partition function zeros form continuous loci in the complex plane.

Boundary conditions significantly influence the shape and location of these loci.

Results enhance understanding of phase transitions in lattice models.

Abstract

We calculate the partition function $Z(G,Q,v)$ of the $Q$-state Potts model exactly for strips of the square and triangular lattices of various widths $L_y$ and arbitrarily great lengths $L_x$, with a variety of boundary conditions, and with $Q$ and $v$ restricted to satisfy conditions corresponding to the ferromagnetic phase transition on the associated two-dimensional lattices. From these calculations, in the limit $L_x \to \infty$, we determine the continuous accumulation loci ${\cal B}$ of the partition function zeros in the $v$ and $Q$ planes. Strips of the honeycomb lattice are also considered. We discuss some general features of these loci.