Sample-to-sample width, which is the thing a disorder run already has

[sotashimozono]

An ensemble of samples gives R_X = Var(X)/[X]² at each size, and the slope of
that says which fixed point the calculation is sitting at. Nothing in the registry
read it, so a disorder run's error bars stayed error bars when they are physics.

StrongSelfAveraging         d ln R_X/d ln L = -d        (L ≫ ξ)
CriticalSelfAveraging       d ln R_X/d ln L = α/ν       (critical, randomness irrelevant)
PseudocriticalWidthScaling  d ln δT_c/d ln L = -1/ν     (random fixed point)

The discriminator, and how close it is

The third is the sharp one. δT_c(L) ∼ L^{-1/ν}, not L^{-d/2}: the latter is
the central-limit answer and holds only where the Harris criterion does, at a pure
fixed point.

They are 2% apart in the case people actually measure. For the site-dilute Ising
model in d = 3 the published exponent is 1.449(8) against d/2 = 1.5, six of
its own errors away, with 1/ν = 1.47. So the test asserts that separation in
units of the measurement's error, not the value: a discriminator this tight is
only useful if the data is good enough to resolve it, and saying so is the point.

Relevant randomness is the case with no law to fit

When the randomness is relevant, R_X does not decay at all. It approaches a
universal non-Gaussian distribution of L-independent width, so more samples at
larger L do not improve the statistics. Both decay relations are refused there
rather than fitted, which is asserted.

Wiseman and Domany originally conjectured R_X ∼ L^{α/ν} with the RANDOM fixed
point's exponents. Aharony and Harris contradict it analytically and the later
simulations contradict it numerically. CriticalSelfAveraging's docstring
therefore says the exponents are the pure system's, and that reading it with the
random ones is that refuted conjecture rather than a variant of it.

Two things worth flagging

Both citations were checked against Crossref rather than written from memory. The
Wiseman-Domany title differs between the preprint and the published version; the
published one is used. This follows a pass where a guessed arXiv id returned an
unrelated quantum Hall paper.

1/ν is not affine in ν, so solve(:ν) needs a specialized _solve. Writing
one in scaling.jl defined a NEW local function rather than extending the
parent's, with no error and no warning, because Criticality did not
import ..AbstractQAtlas: _solve the way StatisticalMechanics already does. It
does now. Worth knowing that this failure mode is silent.

Version

Patch, additive. Three relations, one import, no change to anything existing.

[github-actions]

Reference check — doiget verify

• ✅ resolved: 84
• ☑️ broken (unresolved / malformed): 0

[github-actions]

📚 Docs preview: https://qatlashub.github.io/AbstractQAtlas.jl/previews/PR160/

(updates on each push to this PR)

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.

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