The notion of universality associated with scale invariance has been playing a crucial role in understanding non-equilibrium processes. Systems driven by particle duplication, diffusion and annihilation is one of the most well-studied cases where the notion is particularly useful. In these systems, scale-invariant universal fluctuations can be seen in (a) the vicinity of the critical point of an absorbing-state phase transition, transition into an absorbing state from which escape to other state is impossible, and (b) fluctuating interface of a cluster of particles. For both cases, a variety of systems are categorized into a rather small number of universality classes, two of the most well-known examples being the directed percolation (DP) universality class [1] for absorbing-state phase transitions and Kardar-Parisi-Zhang (KPZ) universality class [2] for fluctuating interfaces.

Empirical observations suggest a relationship between those universal fluctuations. Theoretically, several models in the DP class is known to show the universal fluctuation of the KPZ class far from the critical point.  Experimentally, both of the DP-class fluctuation and the KPZ-class interface fluctuations have been observed in dynamics of topological-defect turbulence in liquid crystal electroconvection [3]. These results suggest that the KPZ-class interface growth generally appears in systems experiencing the DP-class transition. However, the interface fluctuation near the critical point, where the universality in the sense of the DP class arises, is still not well understood.

To shed light on the interplay between those universal fluctuations near the critical point, we conducted extensive numerical simulations of two-dimensional models showing the DP-class transition, in a situation where the active phase, the phase with a nonzero density of particles, is growing from a wall. We found that stochastic properties of the growing phase-boundary interface show a temporal crossover from a region characterized by the exponents of the DP class to a region with the KPZ-class exponents. The similar crossover was also found with the compact DP universality class, another universality class of absorbing-state phase transitions. We further discuss a universal relationship between non-universal parameters of the universality classes.
[1] M. Henkel, H. Hinrichsen, and S. Luebeck, Non-Equilibrium Phase Transitions (2009).
[2] A.-L. Barabási and H. Eugene Stanley, Fractal Concepts in Surface Growth (1995).
[3] K. A. Takeuchi, M. Kuroda, H. Chaté, and M. Sano, Phys. Rev. Lett. 99, 234503 (2007); K. A. Takeuchi and M. Sano, Phys. Rev. Lett. 104, 230601 (2010).