Density of critical clusters in strips of strongly disordered systems

We consider two models with disorder-dominated critical points and study the distribution of clusters that are confined in strips and touch one or both boundaries. For the classical random bond Potts model in the large- q limit, we study optimal Fortuin-Kasteleyn clusters using a combinatorial optimization algorithm. For the random transverse-field Ising chain, clusters are defined and calculated through the strong-disorder renormalization group method. The numerically calculated density profiles close to the boundaries are shown to follow scaling predictions. For the random bond Potts model, we have obtained accurate numerical estimates for the critical exponents and demonstrated that the density profiles are well described by conformal formulas.