Damage spreading in the Potts model with cluster dynamics

We study the Damage Spreading on the two-dimensional ferromagnetic q-state Potts model using Swendsen-Wang dynamics. We find two damage spreading tran sitions: damage does nor spread either at low or high temperatures. At the transition occurring near the Curie temperature our numerical results point through a continuous spreading transition for q less than or equal to 4 an d a discontinuous one for q less than or equal to 5. We also determine the damage critical exponents near the upper spreading temperature threshold (T -s) which seems to be consistent with the directed percolation universality class for all q. (C) 2000 Elsevier Science B.V. All rights reserved.