Departamento de Física, Universidade Federal do Piauí, 64049-550, Teresina

The zero-temperature Glauber dynamics is used to investigate the persistence probability P (t) in the Potts model with Q = 3, 4, 5, 7, 9, 12, 24, 64, 128, 256, 512, 1024, 4096, 16384,..., 230 states on directed and undirected Barabási-Albert networks and Erdös-Rényi random graphs. In this model it is found that P (t) decays exponentially to zero in short times for directed and undirected ErdösRényi random graphs. For directed and undirected Barabási-Albert networks, in contrast it decays exponentially to a constant value for long times, i.e, P (∞) is different from zero for all Q values (here studied) from Q = 3, 4, 5, ..., 230 ; this shows ”blocking” for all these Q values. Except that for Q = 230 in the undirected case P (t) tends exponentially to zero; this could be just a finite-size effect since in the other ”blocking” cases you may have only a few unchanged spins.