Existence of infinite-disorder fixed points in all finite dimensions

Establish whether the random transverse-field Ising model possesses an infinite-disorder fixed point in every finite spatial dimension when the initial disorder is sufficiently strong.

Background

The scaling theory for quantum annealing relies on the strong-disorder renormalization group and therefore on the random transverse-field Ising model flowing to an infinite-disorder fixed point. Numerical studies support this behavior through four dimensions, but the paper notes that corresponding numerical results are unavailable above four dimensions. The authors invoke a conjecture that sufficiently strong disorder produces an infinite-disorder fixed point in every finite dimension, which would justify extending their cluster-fusion description beyond the dimensions directly studied.

References

Although no numerical results are available above $d = 4$, it has been conjectured that discrete-symmetry systems such as the RTFIM have an IDFP in any finite dimension provided the initial disorder is strong enough.

— Quantum annealing of the random transverse-field Ising model in one, two, and three dimensions  (2610.11411 - Kovács et al., 8 Oct 2026) in Section 2.2, “Generalization to higher dimensions”