Softening of Phase Transition in 2D Potts Model Under Quenched Bond Randomness

We have simulated, by using cluster algorithm, the $q=8$ state Potts model in two-dimension with varying amount of quenched bond randomness. We have shown that there exist a finite size dependent threshold value of the introduced quenched bond randomness for rounding the first-order phase transition and this threshold value becomes smaller as the system size increased.