Abstract
We consider two disordered lattice models on the square lattice: on the medial lattice the random field Isingmodel at T = 0 and on the direct lattice the random bond Potts model in the large-q limit at its transition point. The interface properties of the two models are known to berelated by a mapping which is valid in the continuum approximation. Here weconsider finite random samples with the same form of disorder for both modelsand calculate the respective equilibrium states exactly by using combinatorialoptimization algorithms. We study the evolution of the interfaces with the strength ofdisorder and analyse and compare the interfaces of the two models in finite lattices.
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