Phase Transition of the Pair Contact Process Model in a Fragmented Network

We investigate the phase transition of the pair contact process (PCP) model in a fragmented network. The network is formed by rewiring the link between two nearest neighbors to another randomly selected site in one dimension with a probability q. When the average degree < k > = 2, the system exhibits a structure transition and the lattice is fragmented into several isolated subgraphs, it is shown that a giant cluster appears and its node fraction does not change nearly for q > 0. Furthermore, it is found that the critical behavior of the continuous phase transition for the PCP model is different from the directed percolation (DP) class and the estimated values of the critical exponents are independent of the rewiring probability for q > 0. We conjecture that the structure transition for < k > = 2 takes an important role in the change of the critical behavior of the continuous phase transition.