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 $q>1$.
Categories: math-ph cond-mat.stat-mech math.MP math.PR