Critical interfaces in the random-bond Potts model

TL;DR

This paper investigates the geometrical properties of interfaces in the random-temperature Potts model, combining conformal perturbation theory and numerical simulations to analyze fractal dimensions and duality relations.

Contribution

It provides the first analytical computation of the fractal dimension of domain walls in the disordered Potts model and validates these results with numerical simulations.

Findings

Analytical fractal dimension of FK domain walls computed via conformal perturbation theory.

Numerical estimates of spin cluster interface fractal dimensions for q=3.

Confirmation of the duality relation between spin and FK interface parameters.

Abstract

We study geometrical properties of interfaces in the random-temperature q-states Potts model as an example of a conformal field theory weakly perturbed by quenched disorder. Using conformal perturbation theory in q-2 we compute the fractal dimension of Fortuin Kasteleyn domain walls. We also compute it numerically both via the Wolff cluster algorithm for q=3 and via transfer-matrix evaluations. We obtain numerical results for the fractal dimension of spin cluster interfaces for q=3. These are found numerically consistent with the duality kappa(spin) * kappa(FK)= 16 as expressed in putative SLE parameters.