Establish the thermodynamic-limit noise sensitivity of the driven RFIM terminal event

Determine whether the normalized threshold response Q_L=s_L/L^{3/2} and the paired-world terminal-outcome correlation \mathcal S_L(c) converge to zero in the thermodynamic limit for the three-dimensional driven random-field Ising model at disorder strength R=2.16.

Background

The paper derives an exact criterion linking terminal-outcome noise sensitivity to the macroscopic switching response: for a balanced, monotone, transitive Gaussian event, noise sensitivity is equivalent to s_L/L{d/2}\to0. For the three-dimensional driven RFIM, this becomes Q_L=s_L/L{3/2}\to0, equivalently implying that the correlation between outcomes under any fixed nonzero coordinatewise disorder perturbation vanishes.

Simulations at R=2.16 show an overall decrease of both Q_L and the paired-world correlation for the finite sizes studied. However, the authors explicitly state that these observations do not establish the corresponding thermodynamic limits, leaving the asymptotic RFIM behavior unresolved.

References

The data are consistent with the thermodynamic limits $Q_L\to0$ and $\mathcal S_L(c)\to0$, though they do not establish these limits definitively.

— Macroscopic Response Diagnoses the Noise Sensitivity of Terminal Outcomes  (2609.17982 - Li et al., 16 Sep 2026) in Figure 1 caption; Section "Driven-RFIM test"

The narrowing supports noise sensitivity over the simulated range, but we do not infer a universal crossover exponent or a critical disorder value.

— Macroscopic Response Diagnoses the Noise Sensitivity of Terminal Outcomes  (2609.17982 - Li et al., 16 Sep 2026) in Figure 2 caption; Section "Confirmatory finite-noise crossover"