# Potts models with a defect line

## TL;DR

This paper analyzes how a defect line affects correlation length and interface pinning in the ferromagnetic Potts model, extending FK-percolation analysis to arbitrary q>1.

## Contribution

It extends the analysis of FK-percolation to arbitrary q>1, providing detailed insights into defect line effects in the Potts model.

## Key findings

- Correlation length is affected by the defect line at T>T_c.
- A line of weakened bonds pins the interface below critical temperature.
- Results generalize previous Bernoulli percolation analysis.

## Abstract

We provide a detailed analysis of the correlation length in the direction parallel to a line of modified coupling constants in the ferromagnetic Potts model on $\mathbb{Z}^d$ at temperatures $T>T_c$. We also describe how a line of weakened bonds pins the interface of the Potts model on $\mathbb{Z}^2$ below its critical temperature. These results are obtained by extending the analysis by Friedli, Ioffe and Velenik from Bernoulli percolation to FK-percolation of arbitrary parameter $q>1$.