Universal interface fluctuations in absorbing-state phase transitions

TL;DR

This study reveals a universal crossover from absorbing phase transition fluctuations to KPZ growth fluctuations in interface models, linking two key universality classes of nonequilibrium phenomena.

Contribution

It demonstrates that KPZ fluctuation properties emerge universally from APT fluctuations, establishing a fundamental connection between these classes.

Findings

Universal crossover from APT to KPZ fluctuations observed.

Collapse of cumulants onto a single scaling function after rescaling.

KPZ parameters depend solely on APT properties, independent of microscopic details.

Abstract

Despite similarities between models exhibiting absorbing phase transitions (APTs) and those showing Kardar-Parisi-Zhang (KPZ) growth, the relationship between these universal fluctuations has remained elusive. We numerically study (1+1)-dimensional interfaces of (2+1)-dimensional models showing APTs of directed percolation (DP) and compact directed percolation (CDP) classes with an active boundary, finding a universal crossover from short-time APT-governed fluctuations to long-time KPZ fluctuations. Upon rescaling time and length by the APT correlation time and length, the cumulants of the interface height distributions collapse onto a single scaling function. The fluctuation properties of the discrete Domany-Kinzel model and the continuum stochastic Fisher-Kolmogorov-Petrovsky-Piskunov (sFKPP) equation coincide, indicating that the KPZ growth parameters are determined solely by fundamental properties of the APT. For the CDP sFKPP equation, a dimensionless parameter tunes both the critical interface distribution and the KPZ parameters, with the interface properties of the biased voter model recovered in a limiting case. These results uncover a universal crossover in which KPZ fluctuations emerge from APT fluctuations at long times, linking paradigmatic universality classes of nonequilibrium scale-invariant phenomena.