Positive specific-heat critical exponent of a three-dimensional three-state random-bond Potts model

Whereas the stability of a pure critical system is determined by the sign of its specific-heat critical exponent α according to Harrisʼ criterion, whether a d  -dimensional dirty system should satisfy ν⩾2/dν⩾2/d and α<0α<0 or not has been a controversial issue for several decades, where ν   is its correlation-length critical exponent. Here, contrary to recent analytical and numerical results, we find for the three-dimensional three-state random-bond Potts model whose pure version exhibits a first-order phase transition a random fixed point whose ν<2/dν<2/d and α>0α>0 using a finite-time scaling combining with extended dynamic Monte Carlo renormalization-group method. This suggests further studies are still needed to clarify the issue in three-dimensional systems.