Effect of quenched disorder on the absorbing transition in Contact processes on Comb lattice

Priyanka D Bhoyar^1*Prashant M Gade²

• ¹Seth Kesarimal Porwal College of Arts and Science and Commerce, Kamptee, India
• ²Rashtrasant Tukadoji Maharaj Nagpur University, Nagpur, India

The effect of quenched disorder on the absorbing transition in the contact processes is studied on a Comb lattice. Power laws are widely observed in physical, biological, and social systems, often arising near continuous phase transitions characterized by diverging correlation lengths and universal scaling. We study the effect of quenched disorder on the critical dynamics of the contact process on a 1D comb lattice, a minimal model that captures geometric inhomogeneity while remaining analytically and computationally tractable. In our model, activity spreads over a fraction of branches q and is blocked in the rest. Without disorder, the system belongs to the directed percolation (DP) universality class. Introducing disorder alters critical behavior: for q = 0.15, the system exhibits the Griffiths phase with algebraic decay and logarithmic behavior at the criticality, indicating a shift to the activated scaling class. In contrast, when q > 0.15, the contact process on a comb-like lattice exhibits power-law decay for the order parameter only at the critical point, underscoring a clean transition between disorder-induced and standard critical dynamics.