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

Abstract

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.

Phase transitions with infinitely many absorbing states in complex networks

“…At this respect, the apparent non mean-field exponents reported in Ref. [29] for the related pair contact process, a fermionic counterpart of the TCP, can probably be attributed to the networks sizes considered in that work (N 10 4 ), much smaller than the largest system sizes (N ∼ 10 7 ) that we attain here. The CP-HMF universality class studied here can be conjectured to include other CP-like models with a finite or infinite number of absorbing states.…”

“…In the field of complex networks, dynamical systems with many absorbing states have been used to investigate self-organized criticality and avalanches [25][26][27], while the analysis of the ensuing APT is limited to a few works [28,29]. The HMF analysis of the forest fire model in heterogeneous networks yielded critical exponents equal to those obtained for the susceptible-infectedsusceptible epidemic model in the same approach [28].…”

“…The HMF analysis of the forest fire model in heterogeneous networks yielded critical exponents equal to those obtained for the susceptible-infectedsusceptible epidemic model in the same approach [28]. A finite-size scaling [30] analysis of the PCP was performed for homogeneous networks [29], but using very limited sizes, which do not allow to extract reliable conclusions about the model's universality class.…”

Sampling methods for the quasistationary regime of epidemic processes on regular and complex networks

“…However, the behavior of this kind of process is strongly affected by the structure, in the form of a network, that connects the system components and mediate their interactions [10,11]. The former investigations of an epidemic spreading on complex networks [7,[12][13][14], which later revealed many remarkably properties and puzzling outcomes [15][16][17][18][19][20], were subsequently followed by a diversified analysis of other kinds of APTs on networks [6,[21][22][23][24][25][26][27][28].…”