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arXiv · 2605.17781

Universal interface fluctuations in absorbing-state phase transitions

Yohsuke T. Fukai·Keiichi Tamai·Tetsuya Hiraiwa
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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.

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BibTeXRIS

Yohsuke T. Fukai, Keiichi Tamai, Tetsuya Hiraiwa. 2026-05-18. Universal interface fluctuations in absorbing-state phase transitions. https://arxiv.org/abs/2605.17781

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