We have studied the q=8 state Potts model in two dimension to determine the
effects of the distribution of bimodal bonds on the phase transition. We h
ave shown that, by monitoring the energy histograms and autocorrelation tim
es, there exist a finite size-dependent threshold value of the introduced q
uenched bond randomness for rounding the first-order phase transition and t
his threshold value becomes smaller as the system size increased. (C) 1999
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