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 transitions: damage does not 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⩽4 and a discontinuous one for q⩾5. We also determine the damage critical exponents near the upper spreading temperature threshold (Ts) which seems to be consistent with the directed percolation universality class for all q.