Kosterlitz-Thouless transition in planar spin models with bond dilution
  We study the two-dimensional bond-diluted XY and six-state clock models by Monte Carlo simulation with cluster spin updates. Various concentrations of depleted bonds were simulated, in which we found a systematic decrease of the Kosterlitz-Thouless (KT) transition temperatures of both XY and six-state clock models as the concentration of dilution decreases. For the six-state clock model, a second KT transition at lower temperature was observed. The KT transition temperatures as well as the decay exponent $\eta$ for each concentration of dilution are estimated. It is observed that the quasi long range order disappears at the concentration of dilution very close to the percolation threshold. The decay exponent $\eta$ of the KT transitions calculated at each concentration indicates that the universality class belongs to the pure XY and clock models, analogous to the expectation of the Harris criterion for the irrelevance of randomness in the continuous phase transition of systems with non-diverging specific heat. 
Tasrief Surungan and Yukata Okabe