Universality of the antiferromagnetic triangular-lattice long-range transverse-field Ising model

Determine conclusively whether the antiferromagnetic long-range transverse-field Ising model on the triangular lattice remains in the nearest-neighbor three-dimensional XY universality regime for decay exponents extending below the currently supported range.

Background

For antiferromagnetic interactions on the triangular lattice, geometric frustration produces nontrivial critical behavior already in the nearest-neighbor model. The paper summarizes evidence that the nearest-neighbor regime persists for decay exponents approximately greater than one, while also noting that the available evidence does not settle the issue conclusively. The unresolved question concerns the extent and possible breakdown of this universality regime at smaller decay exponents.

References

For the triangular lattice, the situation is not yet resolved conclusively, current literature suggest that the NN regime with 3d XY universality and $z\nu=0.67175(10)$ extends over $\sigma\gtrsim 1$ .

— Exact and fast series expansions for quantum models with long-range interactions  (2609.18761 - Duft et al., 16 Sep 2026) in Figure 15 caption, Section 7.4, “Critical properties from gap extrapolation”