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arxiv: 2604.24789 · v2 · pith:R4HODXR4new · submitted 2026-04-25 · ❄️ cond-mat.stat-mech

Conductance fluctuations in random resistor networks with hyperuniform disorder

Bikram Pal This is my paper

Pith reviewed 2026-05-08 07:02 UTC · model grok-4.3

classification ❄️ cond-mat.stat-mech
keywords conductance fluctuationshyperuniform disorderrandom resistor networksscaling lawsdisordered mediatransport properties
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The pith

Conductance fluctuations in hyperuniform resistor networks scale as L to the power of minus d over 2, the same as in ordinary disorder.

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

The paper investigates whether hyperuniform bond arrangements, which suppress density fluctuations below the usual square-root level, also reduce variations in the total conductance of a random resistor network. Because local conductance responds in proportion to small shifts in bond concentration, a naive expectation is that conductance fluctuations would be damped as well. The authors instead demonstrate that the fluctuations follow the standard central-limit scaling of L to the power of minus d over 2 for a region of linear size L. Numerical checks in two dimensions confirm this result. The finding shows that hyperuniformity does not automatically suppress every fluctuation that involves transport.

Core claim

In random resistor networks with hyperuniform bond disorder, where the number of bonds inside a volume V fluctuates as V to the power of minus a with a greater than one half, the conductance fluctuations still scale as L to the power of minus d over 2 for sampling size L. This scaling persists because small local changes in bond concentration produce a proportionate change in the locally averaged conductance, allowing ordinary central-limit statistics to govern the overall fluctuations.

What carries the argument

Linear response of local conductance to small changes in bond concentration, which converts suppressed number fluctuations into unsuppressed conductance fluctuations.

Load-bearing premise

Small changes in the concentration of bonds present in a local region give rise to a proportionate increase in the locally averaged conductance.

What would settle it

A numerical or experimental measurement that finds conductance fluctuations decaying faster than L to the power of minus d over 2 in a demonstrably hyperuniform resistor network would falsify the claim.

Figures

Figures reproduced from arXiv: 2604.24789 by Bikram Pal.

Figure 1
Figure 1. Figure 1: FIG. 1: The plots above show the spatial distribution of potential (top row) and current (bottom row) for one view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: From left to right, (A) shows model A with view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: From top to bottom we have Model A with view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: (Left) Plot of current-current correlation function view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5 view at source ↗
read the original abstract

We study conductance fluctuations in random resistor networks with hyperuniform bond disorder, where the fluctuations of the number of bonds present in a test volume $V$ scale as $V^{-a}$ with $a > 1/2$. Since small changes in the concentration of bonds present in a local region give rise to a proportionate increase in the locally averaged conductance, one may expect that in hyperuniform disorder, conductance fluctuations will also show suppressed fluctuations. We argue that this is not the case: conductance fluctuations scale as $L^{-d/2}$ for a sampling size $L$. We show numerical results for $d=2$.

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 / 1 minor

Summary. The manuscript examines conductance fluctuations in random resistor networks with hyperuniform bond disorder, where the number of bonds in a volume V fluctuates as V^{-a} with a > 1/2. The authors note that a local proportionality between bond concentration and averaged conductance would naively suggest suppressed conductance fluctuations, but argue instead that fluctuations follow the standard scaling L^{-d/2} for sampling size L. This is supported by numerical results presented for d=2.

Significance. If the central scaling result holds, it demonstrates that hyperuniformity suppresses number fluctuations but does not similarly suppress conductance fluctuations in resistor networks, distinguishing density correlations from transport statistics. This has potential implications for models of conductivity in correlated disordered media and clarifies the limits of naive local averaging arguments in statistical mechanics of transport.

major comments (1)
  1. [Numerical results] Numerical results section: the claim of L^{-d/2} scaling in d=2 is load-bearing for overturning the naive expectation, yet no details are provided on lattice sizes, number of disorder realizations, error bars, or the fitting procedure used to extract the exponent. This absence prevents independent verification of the numerical support.
minor comments (1)
  1. The abstract states the scaling result but does not specify the range of L over which the numerics were performed or how hyperuniformity was implemented in the bond placements.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript, their positive assessment of its significance, and for highlighting the need for greater detail in the numerical results. We address the major comment below and will incorporate the necessary revisions.

read point-by-point responses

  1. Referee: [Numerical results] Numerical results section: the claim of L^{-d/2} scaling in d=2 is load-bearing for overturning the naive expectation, yet no details are provided on lattice sizes, number of disorder realizations, error bars, or the fitting procedure used to extract the exponent. This absence prevents independent verification of the numerical support.

    Authors: We agree that the Numerical results section does not provide sufficient information on the simulation parameters and analysis methods. In the revised manuscript we will expand this section to specify the lattice sizes employed, the number of independent disorder realizations generated for each size, the procedure used to compute error bars, and the fitting method applied to extract the scaling exponent. These additions will enable independent verification of the reported L^{-d/2} scaling. revision: yes

Circularity Check

0 steps flagged

No significant circularity; claim rests on physical argument plus independent numerics

full rationale

The paper's central claim—that conductance fluctuations retain the standard L^{-d/2} scaling despite hyperuniform number fluctuations—is advanced by first stating a physical proportionality assumption (small local bond-concentration changes produce proportionate conductance changes) and then arguing that this does not imply suppressed conductance fluctuations. The counter-claim is supported by numerical results for d=2. No equations, fitted parameters, or self-citations are presented that reduce the scaling result to the input assumption by construction. The derivation therefore remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The claim rests on the domain assumption that local conductance is linearly proportional to local bond density and on the standard definition of hyperuniformity; no free parameters or new entities are introduced in the abstract.

axioms (1)
  • domain assumption Small changes in the concentration of bonds present in a local region give rise to a proportionate increase in the locally averaged conductance
    Explicitly invoked in the abstract as the reason one might expect suppressed fluctuations.

pith-pipeline@v0.9.0 · 5390 in / 1132 out tokens · 77446 ms · 2026-05-08T07:02:05.035360+00:00 · methodology

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Reference graph

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