Softening of the phase transition in a two-dimensional Potts model under quenched bond randomness

We have simulated, by using a cluster algorithm, the [formula presented] state Potts model in two dimensions with a varying amount of quenched bond randomness. We have shown that there exists a finite size-dependent threshold value of the introduced quenched bond randomness for rounding the first-order phase transition and that this threshold value becomes smaller as the system size increases.