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arxiv: 2604.18915 · v1 · submitted 2026-04-20 · ❄️ cond-mat.stat-mech

Coordination-number dependent universality in Mixed Wet Percolation

Jnana Ranjan Das , Santanu Sinha , Alex Hansen , Sitangshu Bikas Santra This is my paper

Pith reviewed 2026-05-10 02:55 UTC · model grok-4.3

classification ❄️ cond-mat.stat-mech
keywords mixed-wet percolationsite percolationcoordination numberuniversalityperimeter clustershullsdual latticetwo-phase flow
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0 comments X

The pith

Mixed-wet percolation follows ordinary site percolation on high-coordination dual lattices but hull scaling on low-coordination ones.

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

The paper studies mixed-wet percolation, in which sites of a primal lattice are occupied at random probability p while bonds appear on the dual lattice only between occupied and unoccupied neighbors. On the dual triangular lattice with coordination number six, the resulting perimeter clusters scale exactly as ordinary site percolation clusters. On the dual honeycomb lattice with coordination number three, the same perimeters instead match the scaling of the hulls of ordinary site percolation clusters. The low coordination number keeps external and internal perimeters separate, yet their union still belongs to the site percolation class. A reader should care because this is an uncommon explicit breakdown of universality inside percolation theory that is tied directly to a single lattice parameter.

Core claim

In mixed-wet percolation the perimeter clusters on the dual triangular lattice (z=6) are the complete boundaries of the occupied site clusters in the primal lattice and therefore belong to the ordinary site percolation universality class. On the dual honeycomb lattice (z=3) the same construction produces isolated external and internal perimeters whose scaling matches that of the hulls of ordinary site percolation clusters; only when external and internal perimeters are combined do they recover the full cluster boundaries of the site percolation class.

What carries the argument

The coordination number z of the dual lattice, which determines whether perimeter clusters formed by mixed-wet bonds act as full site-cluster boundaries or as isolated hulls.

If this is right

  • Perimeter clusters can be used interchangeably with ordinary site clusters when modeling two-phase flow on high-coordination lattices.
  • Low-coordination lattices allow separate measurement of hull and bulk scaling in the same percolation realization.
  • The combined perimeters on low-coordination lattices still belong to the site percolation class, so standard critical exponents remain usable once external and internal contributions are summed.
  • Porous-media simulations must track coordination number when predicting percolation thresholds or cluster statistics under mixed-wet conditions.

Where Pith is reading between the lines

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

  • Real porous media with heterogeneous pore coordination numbers may display position-dependent scaling regimes rather than a single universal class.
  • The result suggests a route to isolate hull statistics experimentally by fabricating low-coordination pore networks.
  • Similar coordination-number effects could appear in other interface or hull models once the dual lattice is allowed to vary.

Load-bearing premise

The difference in scaling behavior is produced by the value of the coordination number rather than by other geometric features that distinguish the triangular and honeycomb lattices.

What would settle it

Observing that perimeter clusters on a different lattice with coordination number three still scale as ordinary site percolation clusters rather than as hulls, or that altering the mixed-wet bond rule while keeping z fixed erases the hull-like scaling on the honeycomb lattice.

Figures

Figures reproduced from arXiv: 2604.18915 by Alex Hansen, Jnana Ranjan Das, Santanu Sinha, Sitangshu Bikas Santra.

Figure 1
Figure 1. Figure 1: FIG. 1. Typical illustrations of the (a) DTL and (b) DHL models. The black circles represent occupied sites, whereas the [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. A morphology of (a) the DTL at [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. A plot of [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. In (a), we plot [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. A plot of cluster size distribution of perimeter bond clusters [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. (a) A plot of the order parameter [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. (a) A plot of the fluctuation [PITH_FULL_IMAGE:figures/full_fig_p009_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. A spanning cluster for (a) DTL and (b) DHL at critical threshold [PITH_FULL_IMAGE:figures/full_fig_p010_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Typical illustrations of the cluster boundary identi [PITH_FULL_IMAGE:figures/full_fig_p010_9.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. In this figure, the data for cluster boundaries on [PITH_FULL_IMAGE:figures/full_fig_p011_11.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. (a) Cluster size distribution [PITH_FULL_IMAGE:figures/full_fig_p011_10.png] view at source ↗
read the original abstract

Mixed-wet percolation was introduced recently in the context of two-phase flow in porous media. In this model, the sites of the primal lattice are occupied with a certain probability $p$, and bonds are placed on the dual lattice between two adjacent occupied and unoccupied sites of the primal lattice. The occupied bonds on the dual lattice form perimeter clusters. In this paper, we investigate the scaling properties of the geometric quantities associated with the perimeter clusters of mixed-wet percolation on the dual triangular and dual honeycomb lattices. Although mixed-wet percolation on the dual triangular lattice with a higher coordination number ($z=6$) exhibits ordinary site percolation, the model on the dual honeycomb lattice with a lower coordination number ($z=3$) exhibits the properties of the hull of ordinary site percolation clusters. Such a $z$ dependent breakdown of universality in mixed-wet percolation is rare in the percolation literature. The perimeter clusters in the triangular lattice represent the boundary of the site clusters in the primal lattice, whereas the perimeters in the honeycomb lattice represent their hulls. Because of the low $z$ of the honeycomb lattice, the external and internal perimeters remain isolated. However, the combined external and internal perimeters form cluster boundaries of the site clusters that belong to the site percolation universality class.

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

1 major / 2 minor

Summary. The manuscript studies mixed-wet percolation, in which primal-lattice sites are occupied with probability p and dual-lattice bonds are placed between adjacent occupied and unoccupied primal sites. It compares the resulting perimeter clusters on the dual triangular lattice (z=6) and dual honeycomb lattice (z=3). The central claim is that the triangular-lattice perimeters belong to the ordinary site-percolation universality class while the honeycomb-lattice perimeters belong to the hull class of ordinary site percolation; this difference is attributed to the lower coordination number on the honeycomb lattice, which isolates external and internal perimeters.

Significance. If the scaling analysis is confirmed and the attribution to coordination number is isolated from other lattice features, the result would constitute a rare documented breakdown of universality within a single percolation family, with direct relevance to two-phase flow modeling in porous media. The explicit distinction drawn between boundary and hull representations of the same primal clusters is a useful geometric clarification.

major comments (1)
  1. [Abstract and concluding discussion] The manuscript attributes the shift from ordinary site-percolation scaling (dual triangular, z=6) to hull scaling (dual honeycomb, z=3) to the value of the coordination number z. However, the comparison is performed on only two lattices whose duality relations, nearest-neighbor angles, and bond-placement rules also differ. No third lattice, no controlled modification of the bond rule that holds geometry fixed while varying z, and no explicit test that the isolation of external and internal perimeters is caused by the numerical value z=3 rather than the three-fold symmetry are presented. This leaves the central title claim of “coordination-number dependent universality” unisolated and therefore load-bearing for the abstract and conclusion.
minor comments (2)
  1. [Abstract] The abstract states that the triangular perimeters “represent the boundary of the site clusters” while the honeycomb perimeters “represent their hulls,” but does not define the precise algorithmic distinction between boundary and hull in the mixed-wet bond-placement rule; a short clarifying sentence or reference to the original mixed-wet paper would help readers.
  2. [Figures] Figure captions and axis labels should explicitly state the measured exponents (e.g., fractal dimension, cluster-size exponent) and the literature values they are compared against, rather than leaving the reader to infer the universality-class assignment solely from visual collapse.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading and for identifying the need to better isolate the coordination-number effect from other lattice properties. We have revised the abstract and concluding discussion to qualify our claims, emphasize the geometric mechanism, and acknowledge the limitations of the two-lattice comparison.

read point-by-point responses

  1. Referee: [Abstract and concluding discussion] The manuscript attributes the shift from ordinary site-percolation scaling (dual triangular, z=6) to hull scaling (dual honeycomb, z=3) to the value of the coordination number z. However, the comparison is performed on only two lattices whose duality relations, nearest-neighbor angles, and bond-placement rules also differ. No third lattice, no controlled modification of the bond rule that holds geometry fixed while varying z, and no explicit test that the isolation of external and internal perimeters is caused by the numerical value z=3 rather than the three-fold symmetry are presented. This leaves the central title claim of “coordination-number dependent universality” unisolated and therefore load-bearing for the abstract and conclusion.

    Authors: We agree that the comparison is restricted to two standard dual lattices and that other geometric features (symmetry, angles) necessarily differ. The bond-placement rule itself is identical by definition of mixed-wet percolation. The manuscript’s geometric argument is that z=3 on the honeycomb dual isolates external and internal perimeters (producing hull scaling), while z=6 permits their merger into ordinary boundaries. This mechanism is tied to the numerical value of z in these lattices, but we acknowledge that a controlled variation at fixed geometry or a third lattice would be required to fully separate z from symmetry. We have therefore revised the abstract and conclusion to state that the results “suggest” a coordination-number-dependent breakdown of universality, to remove the stronger title phrasing from the abstract, and to add an explicit caveat on the two-lattice limitation. These changes address the referee’s concern while remaining faithful to the evidence presented. revision: partial

Circularity Check

0 steps flagged

No significant circularity; scaling claims rest on independent lattice comparisons

full rationale

The paper reports numerical observations of perimeter-cluster scaling on two distinct dual lattices (triangular z=6 vs. honeycomb z=3) under the mixed-wet bond-placement rule. The central statements—that one case matches ordinary site percolation while the other matches hull scaling—are presented as direct consequences of the model definitions on each lattice geometry, without any derivation, equation, or fitted parameter that reduces the reported universality-class difference to a tautology or to the input data by construction. Background citations to the model's recent introduction are not load-bearing for the new z-dependent claim. The analysis therefore remains self-contained and externally falsifiable via independent simulation on the same lattices.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The paper extends a recently introduced mixed-wet percolation model to two specific lattices and relies on standard percolation scaling assumptions without introducing new fitted parameters or postulated entities.

axioms (2)
  • domain assumption Random site occupation with probability p on a lattice defines the mixed-wet configuration.
    This is the definition of the model stated in the abstract.
  • domain assumption Perimeter clusters are formed by dual-lattice bonds between occupied and unoccupied primal sites.
    Core geometric construction used to define the clusters whose scaling is measured.

pith-pipeline@v0.9.0 · 5534 in / 1202 out tokens · 45448 ms · 2026-05-10T02:55:51.539244+00:00 · methodology

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Reference graph

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