Effect of quenched disorder on the absorbing transition in contact processes on a comb lattice

Power-law behavior frequently emerges in physical, biological, and social systems, particularly near continuous phase transitions characterized by diverging correlation lengths and universal scaling. The contact process is a prototypical model for studying absorbing-state phase transitions, typically belonging to the directed percolation (DP) universality class in its clean form. In this study, we investigate how quenched disorder influences the absorbing-state transition of the contact process on a one-dimensional comb lattice, a minimal geometry that incorporates structural inhomogeneity while remaining analytically and computationally tractable. In our model, activity spreads over a fraction of the branches q and is blocked in the rest. Without disorder, the system belongs to the directed percolation (DP) universality class. Introducing quenched disorder leads to significant changes in the critical dynamics. For q≤0.15, the system develops a Griffiths phase characterized by algebraic decay away from the critical point and logarithmic scaling at criticality, indicating a transition to the activated scaling universality class. In contrast, for q>0.15, the contact process on the comb lattice shows power-law decay of the order parameter only at the critical point, demonstrating a clean transition with standard critical dynamics and no extended Griffiths region. The results show that quenched disorder induces non-universal slow dynamics for small q, while larger values of q suppress the disorder-driven effects, restoring standard DP-like criticality. This transition underscores the role of lattice geometry and disorder strength in shaping nonequilibrium phase transitions.