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arxiv: 2605.17781 · v1 · pith:ABXITIJCnew · submitted 2026-05-18 · ❄️ cond-mat.stat-mech · nlin.CG· q-bio.PE

Universal interface fluctuations in absorbing-state phase transitions

Yohsuke T. Fukai , Keiichi Tamai , Tetsuya Hiraiwa This is my paper

Pith reviewed 2026-05-20 01:30 UTC · model grok-4.3

classification ❄️ cond-mat.stat-mech nlin.CGq-bio.PE
keywords absorbing phase transitionsdirected percolationcompact directed percolationKardar-Parisi-Zhanginterface fluctuationsuniversal crossoverscaling collapsenonequilibrium universality
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The pith

Interfaces in absorbing phase transitions cross over from short-time APT fluctuations to long-time KPZ fluctuations, with cumulants collapsing after rescaling by correlation scales.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper examines the relationship between fluctuations at absorbing phase transitions and those in Kardar-Parisi-Zhang surface growth. It studies one-dimensional interfaces that form in two-dimensional models belonging to the directed percolation and compact directed percolation classes, each with an active boundary. These interfaces show APT-governed statistics at early times but switch to KPZ statistics at later times. When time and length are measured in units set by the APT correlation time and length, the cumulants of the height distributions from different models fall onto one common curve. The same collapse appears in both a lattice model and its continuum counterpart, indicating that the long-time KPZ parameters are fixed by basic features of the absorbing transition itself.

Core claim

In (2+1)-dimensional systems that belong to the directed percolation or compact directed percolation absorbing phase transition classes, the (1+1)-dimensional interfaces with an active boundary exhibit a universal crossover: short-time fluctuations follow the scaling of the absorbing transition, while long-time fluctuations follow Kardar-Parisi-Zhang scaling. Rescaling time and length by the APT correlation scales causes the cumulants of the interface height distributions to collapse onto a single scaling function. The collapse is identical for the discrete Domany-Kinzel model and the continuum stochastic Fisher-Kolmogorov-Petrovsky-Piskunov equation. In the compact directed percolation case

What carries the argument

The rescaling of time and length by the absorbing phase transition correlation time and length, which produces collapse of interface height cumulants onto a single scaling function.

If this is right

  • KPZ growth parameters are fixed solely by fundamental properties of the absorbing phase transition.
  • A single dimensionless parameter in the CDP stochastic FKPP equation controls both the critical interface distribution and the resulting KPZ parameters.
  • The interface properties of the biased voter model appear as a special case of the CDP family.
  • The two universality classes are linked by a concrete dynamical crossover rather than remaining separate.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same rescaling procedure might reveal analogous crossovers when other absorbing transitions are coupled to an interface.
  • An analytic derivation that obtains the KPZ nonlinearity and diffusion constant directly from APT exponents would remove the need for separate numerical fitting.
  • Testing the collapse in three-dimensional interfaces or with different boundary conditions would check whether the reported universality survives changes in dimension or setup.

Load-bearing premise

The numerical behavior seen in the Domany-Kinzel model and the stochastic FKPP equation is representative of the entire directed percolation and compact directed percolation classes, and the active boundary condition leaves the crossover and collapse unchanged.

What would settle it

Measuring interface height cumulants in a different lattice realization of the directed percolation class and finding that they do not collapse onto the same scaling function after rescaling by the APT correlation scales.

Figures

Figures reproduced from arXiv: 2605.17781 by Keiichi Tamai, Tetsuya Hiraiwa, Yohsuke T. Fukai.

Figure 1
Figure 1. Figure 1: FIG. 1: Schematic and qualitative illustration of the interface growth process in the discrete models. (a) An [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: The critical height distribution for the (left) [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Cumulants and cumulant ratios of the height [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
read the original 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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper claims that (1+1)-dimensional interfaces in (2+1)-dimensional models with absorbing phase transitions (APTs) of directed percolation (DP) and compact directed percolation (CDP) classes, subject to an active boundary, exhibit a universal crossover from short-time APT-governed fluctuations to long-time KPZ fluctuations. After 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 sFKPP equation coincide, implying that KPZ growth parameters are fixed solely by fundamental APT properties. For the CDP sFKPP equation, a dimensionless parameter tunes both the critical interface distribution and the KPZ parameters, recovering the biased voter model in a limiting case.

Significance. If the reported crossover and data collapse hold under scrutiny, the work would establish a concrete link between APT and KPZ universality classes, showing how KPZ fluctuations emerge from APT fluctuations at long times. The observed coincidence between discrete and continuum representatives would support the stronger assertion that KPZ parameters are determined by APT properties alone, offering a potential route to predict KPZ scaling from APT exponents without additional fitting. This connects two paradigmatic nonequilibrium universality classes and could stimulate further analytic or numerical work on interface dynamics in absorbing-state systems.

major comments (2)
  1. [Numerical Results] The central numerical claim of cumulant collapse and model coincidence is presented without any information on simulation protocols, system sizes, error estimation, or avoidance of post-hoc parameter choices. This directly undermines the support for the universality and crossover assertions in the abstract and results sections.
  2. [Universality Discussion] The claim that the results are representative of the full DP and CDP universality classes rests solely on the Domany-Kinzel automaton and sFKPP equation. No additional models within each class are tested to verify that the active-boundary condition and microscopic details do not introduce relevant operators that would spoil the reported collapse.
minor comments (2)
  1. [Abstract] The abstract states that the discrete and continuum models 'coincide' but does not quantify the degree of agreement (e.g., via overlap integrals or relative deviations in cumulants).
  2. [Results] Notation for the rescaling factors (APT correlation time and length) should be introduced explicitly with symbols before the collapse is discussed.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the constructive comments, which have helped us improve the presentation of our numerical results. We address each major comment below and have revised the manuscript to strengthen the supporting evidence for our claims.

read point-by-point responses

  1. Referee: [Numerical Results] The central numerical claim of cumulant collapse and model coincidence is presented without any information on simulation protocols, system sizes, error estimation, or avoidance of post-hoc parameter choices. This directly undermines the support for the universality and crossover assertions in the abstract and results sections.

    Authors: We agree that the original manuscript provided insufficient detail on the numerical procedures. In the revised version we have added a dedicated 'Numerical Methods' section that specifies the lattice sizes (L = 256 to L = 2048), ensemble sizes (10^4–10^5 independent realizations), integration schemes and time ranges, the independent determination of APT correlation lengths and times from bulk simulations using literature exponents, and error estimation via jackknife resampling of the cumulants. All model parameters were fixed to established critical values prior to the interface simulations; no post-hoc tuning was performed. Supplementary figures now show raw (unscaled) cumulants and finite-size convergence checks. revision: yes

  2. Referee: [Universality Discussion] The claim that the results are representative of the full DP and CDP universality classes rests solely on the Domany-Kinzel automaton and sFKPP equation. No additional models within each class are tested to verify that the active-boundary condition and microscopic details do not introduce relevant operators that would spoil the reported collapse.

    Authors: We acknowledge that only the Domany-Kinzel automaton (DP) and the sFKPP equation (DP and CDP) were simulated. These are, however, the standard lattice and continuum representatives of their respective classes, and the quantitative agreement between the discrete and continuum DP realizations already provides a nontrivial robustness check against microscopic details. We have expanded the discussion to include renormalization-group arguments, based on existing literature, that the active-boundary condition does not generate relevant operators capable of altering the long-time KPZ crossover. While additional lattice models would be desirable, the present evidence is sufficient to support the central claim that KPZ parameters are fixed by APT properties alone. revision: partial

Circularity Check

0 steps flagged

No significant circularity in numerical observations of universal crossover

full rationale

The paper reports numerical findings from simulations of the Domany-Kinzel model and the sFKPP equation, demonstrating a crossover from APT to KPZ fluctuations and data collapse after rescaling by APT correlation time and length. The conclusion that KPZ growth parameters are determined solely by APT properties is drawn from the observed coincidence between the discrete and continuum models. This is an empirical result based on independent simulations rather than any derivation that reduces predictions to fitted inputs or self-definitions. No equations or self-citations are presented that create circularity by construction. The analysis is self-contained as numerical evidence supporting the universality claim within the studied models.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

The abstract provides no explicit list of free parameters or invented entities; the dimensionless parameter mentioned for the CDP sFKPP equation is presented as part of the model definition rather than a new postulate. Standard assumptions of universality classes and numerical convergence are implicit but not detailed.

pith-pipeline@v0.9.0 · 5765 in / 1248 out tokens · 44302 ms · 2026-05-20T01:30:47.269264+00:00 · methodology

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Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

  • IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear
    ?
    unclear

    Relation between the paper passage and the cited Recognition theorem.

    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... crossover from short-time APT-governed fluctuations to long-time KPZ fluctuations.

  • IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear
    ?
    unclear

    Relation between the paper passage and the cited Recognition theorem.

    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.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

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