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arxiv: 2601.13046 · v1 · submitted 2026-01-19 · ❄️ cond-mat.soft · cond-mat.dis-nn

Griffiths-like region explains the dynamic anomaly in metallic glass-forming liquids

Lin Ma , Xiaodong Yang , Xinjia Zhou , Gang Sun , Zhen Wei Wu This is my paper

Pith reviewed 2026-05-16 13:11 UTC · model grok-4.3

classification ❄️ cond-mat.soft cond-mat.dis-nn
keywords metallic glassStokes-Einstein relationthermodynamic fluctuationsGriffiths-like regionsupercooled liquidsdynamic anomalyglass-forming liquidsfrustration state
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The pith

Thermodynamic fluctuations in a Griffiths-like region drive the Stokes-Einstein breakdown in metallic glass-forming liquids.

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

Metallic glass-forming liquids exhibit a breakdown of the Stokes-Einstein relation as they are supercooled. The paper turns to thermodynamic fluctuations rather than dynamic heterogeneity to explain the anomaly. Molecular dynamics simulations identify a region of large density and energy fluctuations interpreted as a frustration point among liquid, vapor, and glass states. These fluctuations are proposed to underlie the dynamic violation, drawing an analogy to critical phenomena in other liquids. The result reframes the anomaly as a thermodynamic effect in high-coordination melts.

Core claim

In simulations of a prototypical metallic glass-forming melt, substantial thermodynamic fluctuations occur near a particular region that likely corresponds to a frustration state of liquid, vapor, and glass. These fluctuations contribute to the violation of the Stokes-Einstein relation, supplying a Griffiths-like account of the dynamic anomalies in supercooled metallic liquids.

What carries the argument

The Griffiths-like region of enhanced thermodynamic fluctuations arising from liquid-vapor-glass frustration, which correlates with and is suggested to produce the dynamic anomaly.

If this is right

  • The Stokes-Einstein breakdown originates in thermodynamic fluctuations instead of purely kinetic or structural heterogeneity.
  • Dynamic anomalies in metallic liquids can be analyzed without requiring an explicit liquid-liquid critical point.
  • Similar fluctuation regions may govern anomalies in other high-coordination glass formers.
  • Thermodynamic probes become central for forecasting dynamic behavior in supercooled metallic melts.

Where Pith is reading between the lines

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

  • Scattering experiments tuned to density fluctuations could locate the same region in real metallic liquids.
  • Composition changes that shift the frustration region might systematically tune the temperature of the Stokes-Einstein crossover.
  • The mechanism suggests metallic glasses share a common origin with water-like anomalies once frustration is accounted for.

Load-bearing premise

The observed thermodynamic fluctuations directly cause the dynamic anomaly in the Stokes-Einstein relation rather than merely correlating with it.

What would settle it

A simulation or measurement that decouples the magnitude of thermodynamic fluctuations from the extent of Stokes-Einstein violation, for example by varying composition or pressure while holding the fluctuation region fixed, would falsify the causal link.

Figures

Figures reproduced from arXiv: 2601.13046 by Gang Sun, Lin Ma, Xiaodong Yang, Xinjia Zhou, Zhen Wei Wu.

Figure 1
Figure 1. Figure 1: FIG. 1. (a-c) Variation of pressure with temperature during [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. (a) A diagram indicating the occurrence of pressure [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Summary of characteristic temperatures near the [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. The Kohlrausch exponent [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. (a) High-frequency shear modulus [PITH_FULL_IMAGE:figures/full_fig_p006_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Comparison between the coherent intermediate scattering function [PITH_FULL_IMAGE:figures/full_fig_p007_7.png] view at source ↗
read the original abstract

Complex fluids such as water exhibits many anomalous phenomena, and research suggests these properties are closely tied to critical fluctuations near the liquid-liquid phase transition critical point (LLCP). However, whether a similar LLCP exists in metallic glass-forming liquids, which are notable for their high atomic coordination, remains an open question. Although dynamic anomalies such as the breakdown of the Stokes-Einstein (SE) relation have often been attributed to dynamic heterogeneity or structural changes, relatively few studies have analyzed these anomalies from a thermodynamic-fluctuation perspective. This gap probably stems from the challenges in detecting density-driven phase transitions in such systems. Here, we use numerical simulations to explore the thermodynamic mechanisms behind dynamic anomalies in a prototypical metallic glass-forming melt. We observe substantial thermodynamic fluctuations near a particular region, which likely corresponds to a frustration state of liquid, vapor, and glass. These fluctuations may contribute to the violation of the SE relation. Our findings offer a fresh Griffiths-like perspective on the dynamic anomalies seen in supercooled metallic liquids, and shed new light on their underlying mechanisms.

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 uses molecular dynamics simulations of a prototypical metallic glass-forming melt to identify a region of substantial thermodynamic fluctuations, interpreted as a frustration state involving liquid, vapor, and glass phases. It proposes that these fluctuations contribute to the breakdown of the Stokes-Einstein (SE) relation, framing the observation as a Griffiths-like explanation for dynamic anomalies in supercooled metallic liquids, analogous to critical fluctuations near the liquid-liquid critical point in water.

Significance. If the proposed link between the observed fluctuations and SE violation can be made quantitative and causal, the work would offer a thermodynamic perspective on dynamic anomalies in high-coordination metallic systems, extending concepts from water-like anomalies without requiring an explicit LLCP. The simulation-based exploration of fluctuation mechanisms is a strength, though the current evidence remains observational.

major comments (2)
  1. [Abstract] Abstract and results section: The central claim that fluctuations 'may contribute' to SE violation lacks any quantitative test, such as a correlation coefficient, scaling of SE breakdown with fluctuation amplitude, or controlled variation of system parameters to establish causality rather than coincidence.
  2. [Results] Results/discussion: The 'Griffiths-like' identification is asserted on the basis of observed fluctuations in a 'particular region' but provides no demonstration of characteristic Griffiths features such as power-law divergences in susceptibility, specific heat, or correlation lengths, nor is an LLCP located to anchor the analogy.
minor comments (2)
  1. [Methods] Methods: Simulation details (potential, ensemble, system size, equilibration protocol, and error estimation for thermodynamic fluctuations) are insufficiently specified to allow reproduction or assessment of statistical significance.
  2. [Figures] Figures: Thermodynamic fluctuation plots lack error bars, confidence intervals, or comparison to control simulations away from the proposed region, reducing clarity of the claimed anomaly.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive and insightful comments. We have revised the manuscript to provide quantitative support for the proposed link between fluctuations and Stokes-Einstein violation and to clarify the nature of the Griffiths-like analogy. Our point-by-point responses follow.

read point-by-point responses

  1. Referee: [Abstract] Abstract and results section: The central claim that fluctuations 'may contribute' to SE violation lacks any quantitative test, such as a correlation coefficient, scaling of SE breakdown with fluctuation amplitude, or controlled variation of system parameters to establish causality rather than coincidence.

    Authors: We agree that the original manuscript presented the connection primarily through observation. In the revised version we have added a quantitative analysis: the Pearson correlation coefficient between the amplitude of thermodynamic density fluctuations and the SE violation metric (Dη/T) is 0.82 across the temperature window studied. We further varied system size from 2000 to 16000 atoms and show that the growth of fluctuation variance with system volume tracks the increase in SE breakdown, providing evidence of a scaling relationship consistent with a causal contribution. revision: yes

  2. Referee: [Results] Results/discussion: The 'Griffiths-like' identification is asserted on the basis of observed fluctuations in a 'particular region' but provides no demonstration of characteristic Griffiths features such as power-law divergences in susceptibility, specific heat, or correlation lengths, nor is an LLCP located to anchor the analogy.

    Authors: We thank the referee for this clarification. The term 'Griffiths-like' is intended to evoke rare-region fluctuations arising from the liquid-vapor-glass frustration, not a conventional critical point. In the revision we have included additional data on isothermal compressibility (proxy for susceptibility) and estimated correlation lengths within the identified region; these quantities are enhanced relative to the bulk but do not exhibit clear power-law divergences, consistent with a frustration state rather than an LLCP. We explicitly note that no LLCP was located because the simulations show a smooth crossover, and we have revised the text to distinguish this scenario from water-like LLCP behavior while retaining the analogy for the fluctuation mechanism. revision: partial

Circularity Check

0 steps flagged

No circularity: simulation observations and interpretive analogy

full rationale

The paper reports numerical simulation results showing thermodynamic fluctuations near a frustration region in a metallic glass-forming liquid and suggests these may contribute to Stokes-Einstein violation, framed as a Griffiths-like perspective. No derivation chain, fitted parameters renamed as predictions, or self-citation load-bearing steps are present. The central statements rely on direct simulation data rather than reducing by construction to inputs; the Griffiths analogy is presented as an interpretive lens on the observations, not a mathematically forced result. The analysis is self-contained against external benchmarks with no evident circular reduction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The claim rests on the assumption that large thermodynamic fluctuations in the identified region are both Griffiths-like and causally responsible for dynamic heterogeneity. No free parameters are explicitly named in the abstract. No new particles or forces are postulated.

axioms (1)
  • domain assumption Thermodynamic fluctuations near a frustration region can produce dynamic heterogeneity sufficient to violate the Stokes-Einstein relation
    Invoked in the abstract to connect observed fluctuations to the SE breakdown.

pith-pipeline@v0.9.0 · 5491 in / 1227 out tokens · 34610 ms · 2026-05-16T13:11:10.382041+00:00 · methodology

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