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arxiv: 2604.11476 · v1 · submitted 2026-04-13 · ❄️ cond-mat.dis-nn · cond-mat.stat-mech

Recognition: unknown

Nexus-CAT: A Computational Framework to Define Long-Range Structural Descriptors in Glassy Materials from Percolation Theory

Julien Perradin , Simona Ispas , Anwar Hasmy , Bernard Hehlen
Authors on Pith no claims yet

Pith reviewed 2026-05-10 15:05 UTC · model grok-4.3

classification ❄️ cond-mat.dis-nn cond-mat.stat-mech
keywords percolation theoryglassy materialscluster analysisamorphous siliconcomputational toolkitvitreous silicastructural descriptors
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The pith

Nexus-CAT detects a percolation transition in amorphous silicon prior to crystallization.

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

The paper presents Nexus-CAT, a Python toolkit for analyzing clusters and percolation in glassy material simulations to capture long-range structural changes missed by conventional tools. It implements a Union-Find algorithm with four clustering strategies tailored to different network types and a precise method for detecting percolation in periodic systems. Validation on vitreous silica, ice, and silicon reveals that in amorphous silicon, a percolation event happens before crystallization under pressure, pointing to an initial amorphous phase transformation with similar coordination. This framework allows quantitative study of connectivity in disordered systems and is designed for extension to other materials like gels.

Core claim

Nexus-CAT is a computational framework that uses percolation theory to define long-range structural descriptors in glassy materials. By applying cluster analysis to atomistic trajectories, it identifies percolation transitions, with the original finding being a percolation transition prior to crystallization in amorphous silicon, indicating that pressure-induced crystallization begins with an amorphous transformation sharing the same coordination number.

What carries the argument

Union-Find algorithm with path-compression for cluster detection, combined with a Strategy Factory implementing distance-based, bonding, coordination-filtered, and shared-neighbor clustering, plus a period vector algorithm for percolation detection in periodic boundaries.

If this is right

  • The toolkit can be used to study amorphous-amorphous transitions in various glasses by quantifying long-range connectivity.
  • It provides validated methods for computing percolation properties in simulated networks of silica, ice, and silicon.
  • The code supports extension to gels, cements, and other disordered materials for similar analyses.
  • Standard structural descriptors like pair distribution functions are supplemented by these percolation-based metrics.

Where Pith is reading between the lines

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

  • Linking percolation to mechanical or optical properties could offer new ways to predict glass behavior under stress.
  • Applying the same clustering strategies to experimental data from scattering techniques might bridge simulation and observation.
  • Exploring different pressure or temperature paths in silicon could test if the percolation always precedes crystallization.

Load-bearing premise

The clustering strategies accurately represent the true physical connectivity in the atomic networks without being skewed by arbitrary distance cutoffs or boundary conditions.

What would settle it

A simulation of amorphous silicon under pressure where the coordination number changes or crystallization starts without a detectable percolation transition in the cluster analysis would challenge the observation.

Figures

Figures reproduced from arXiv: 2604.11476 by Anwar Hasmy, Bernard Hehlen, Julien Perradin, Simona Ispas.

Figure 1
Figure 1. Figure 1: Typical workflow of Nexus-CAT python package (attribute and method names are not those used in the program [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Representation of the different strategies applied to amorphous SiO [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Performance benchmark of the Nexus-CAT package [PITH_FULL_IMAGE:figures/full_fig_p016_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: a shows the correlation length as a function of occupation prob￾ability p for each system size; each curve depicts a maximum whose location tends to the theoretical percolation threshold for 3D site percolation on a simple cubic lattice pc ≃ 0.3116 [32]. Via the finite-size scaling ansatz [36], one can extract the critical exponents at the percolation threshold if the con￾dition ξ ∝ L is respected and comp… view at source ↗
Figure 4
Figure 4. Figure 4: Finite-size scaling analysis of cluster properties. Scaling laws of [PITH_FULL_IMAGE:figures/full_fig_p018_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Percolation transitions in v-SiO2 under compression. a) Correlation length ξ of SiO4-SiO4 (circles), SiO5-SiO5 (squares), SiO6-SiO6 (diamonds), and SiO6*-SiO6 (triangles) with 7 system sizes N = 1008, 3024, 8064, 15120, 27216, 96000 and 1056000 atoms in red, orange, yellow, lime, cyan, blue, purple, respectively. b) Order parameter P∞ (symbols) and SiOZ fractions ϕ (colored lines) as a function of pressure… view at source ↗
Figure 6
Figure 6. Figure 6: Percolation transitions in amorphous silicon under compression using original [PITH_FULL_IMAGE:figures/full_fig_p023_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Percolation transitions in amorphous ice under compression at 124K. Full lines [PITH_FULL_IMAGE:figures/full_fig_p024_7.png] view at source ↗
read the original abstract

Nexus-CAT (Cluster Analysis Toolkit) is an open-source Python package for cluster detection and percolation analysis of atomistic simulation trajectories. Standard structural tools, such as the pair distribution function or structure factor, fail to capture the long-range connectivity changes underlying amorphous-amorphous transitions in glassy materials. Nexus-CAT addresses this gap by reading extended XYZ trajectory files and identifying clusters via a Union-Find algorithm with path-compression. Four clustering strategies, i.e., distance-based, bonding, coordination-filtered, and shared-neighbor, are implemented through a Strategy Factory design pattern, enabling the treatment of diverse network topologies. The program computes key percolation properties with percolation detection based on a rigorous period vector algorithm. The package is validated against theoretical predictions and applied to glasses with different bonding environments, namely vitreous silica, vitreous ice, and amorphous silicon. One original result is the observation of a percolation transition prior to crystallization in the latter, indicating that pressure-induced crystallization is initially driven by an amorphous transformation with similar coordination number. The code is also designed to be readily extended to gels, cements, and other disordered materials. Nexus-CAT is fully available on GitHub and PyPI.

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 manuscript introduces Nexus-CAT, an open-source Python package for cluster detection and percolation analysis of atomistic simulation trajectories in glassy materials. It implements a Union-Find algorithm with path compression and four clustering strategies (distance-based, bonding, coordination-filtered, shared-neighbor) via a Strategy Factory pattern. The package computes percolation properties using a period-vector algorithm, is validated against theoretical predictions, and is applied to vitreous silica, vitreous ice, and amorphous silicon. An original result reported is the observation of a percolation transition prior to crystallization in a-Si, interpreted as indicating that pressure-induced crystallization begins via an amorphous transformation with similar coordination number. The code is released on GitHub and PyPI and designed for extension to other disordered systems.

Significance. If the results hold, the work supplies a practical, extensible tool for extracting long-range connectivity descriptors in amorphous networks where pair-distribution functions and structure factors are insufficient. The open-source release, Strategy Factory design, and rigorous period-vector percolation test are clear strengths that enable reproducible analysis and community extension to gels, cements, and similar materials. The multi-system application demonstrates versatility, and the a-Si finding, if substantiated, would offer mechanistic insight into pressure-driven crystallization pathways.

major comments (2)
  1. [Application to amorphous silicon] Application to amorphous silicon: The reported percolation transition prior to crystallization depends on connectivity defined by one of the four strategies, yet no sensitivity analysis is presented for the cutoff parameters (distance threshold, neighbor criterion, etc.). A modest change in these values can shift or remove the apparent transition, and the period-vector test inherits any such misidentification; this directly affects the load-bearing claim that the process is initially driven by an amorphous-amorphous change.
  2. [Validation] Validation and methods: While the package is stated to be validated against theoretical predictions, the validation does not include cross-checks (e.g., ring statistics or bond-orientational order) confirming that clusters identified by the four strategies correspond to physically relevant medium-range order rather than cutoff-induced artifacts in the a-Si trajectories.
minor comments (2)
  1. [Figures] Figure captions should explicitly state the clustering strategy and cutoff values used for each panel to allow immediate reproducibility.
  2. [Abstract] The abstract could more precisely indicate which of the four strategies produced the a-Si percolation result.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed comments. We address each major comment point by point below, indicating the revisions we will incorporate to strengthen the manuscript.

read point-by-point responses

  1. Referee: [Application to amorphous silicon] Application to amorphous silicon: The reported percolation transition prior to crystallization depends on connectivity defined by one of the four strategies, yet no sensitivity analysis is presented for the cutoff parameters (distance threshold, neighbor criterion, etc.). A modest change in these values can shift or remove the apparent transition, and the period-vector test inherits any such misidentification; this directly affects the load-bearing claim that the process is initially driven by an amorphous-amorphous change.

    Authors: We agree that sensitivity analysis is necessary to substantiate the robustness of the percolation transition in a-Si. The manuscript selects parameters based on the known coordination and bonding in amorphous silicon, but we acknowledge that explicit tests were not included. In the revised manuscript we will add a sensitivity study varying the distance threshold, neighbor criterion, and related cutoffs within physically motivated ranges, demonstrating that the percolation transition persists and is not an artifact of a single parameter choice. This analysis will be presented in the main text or supplementary material to support the interpretation of an initial amorphous-amorphous transformation. revision: yes

  2. Referee: [Validation] Validation and methods: While the package is stated to be validated against theoretical predictions, the validation does not include cross-checks (e.g., ring statistics or bond-orientational order) confirming that clusters identified by the four strategies correspond to physically relevant medium-range order rather than cutoff-induced artifacts in the a-Si trajectories.

    Authors: The existing validation confirms that the Union-Find implementation and period-vector percolation algorithm reproduce exact theoretical thresholds on model lattices and simple networks. For the a-Si application, the four strategies incorporate physical criteria (coordination filtering, bonding definitions) intended to capture relevant connectivity. To address the concern about possible artifacts, the revised manuscript will include additional cross-checks comparing the identified clusters against ring statistics and bond-orientational order parameters (such as Steinhardt Q6) computed on the same trajectories. These comparisons will be added to the validation section to demonstrate that the clusters align with established medium-range order descriptors rather than arising solely from cutoff choices. revision: yes

Circularity Check

0 steps flagged

No circularity: standard algorithms applied to external trajectories

full rationale

The manuscript describes an open-source Python package implementing established algorithms (Union-Find with path compression, period-vector percolation test) on pre-existing atomistic trajectories. No equations, predictions, or central claims are derived from fitted parameters, self-referential definitions, or load-bearing self-citations within the paper. The four clustering strategies are presented as alternative implementations via a design pattern, not as results that reduce to their own inputs. Validation against external theoretical predictions and application to independent simulation data (vitreous silica, ice, a-Si) keeps the framework self-contained; no step equates a claimed outcome to its own construction.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The framework rests on standard computer-science algorithms and domain-standard assumptions about periodic boundary conditions and connectivity definitions; no new physical entities or fitted parameters are introduced in the abstract description.

axioms (2)
  • standard math Union-Find with path compression correctly partitions atoms into disjoint clusters
    Standard disjoint-set data structure whose correctness is established in computer science.
  • domain assumption Period-vector algorithm accurately identifies spanning clusters under periodic boundary conditions
    Assumes the percolation detection routine handles simulation box periodicity without error.

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