Persistence In The Zero-Temperature Dynamics Of The Q-States Potts Model Undirected-Directed Barabasi-Albert Networks And Erdos-Renyi Random Graphs

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, 16 384, ... , 2(30) states on directed and undirected Barabasi-Albert networks and Erdos-Renyi (ER) random graphs. In this model, it is found that P(t) decays exponentially to zero in short times for directed and undirected ER random graphs. For directed and undirected BA networks, in contrast it decays exponentially to a constant value for long times, i. e., P(infinity) is different from zero for all Q values (here studied) from Q = 3; 4; 5, ..., 2(30); this shows "blocking" for all these Q values. Except that for Q = 2(30) 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.