  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.
