Determine whether quenched disorder preserves homogeneous layering transitions

Determine whether the first-order layering-transition structure of the homogeneous two-dimensional SOS wetting model persists in the presence of quenched disorder, despite the unbounded SOS height variable and the direct coupling of disorder to the wall-contact observable.

Background

The paper proves that, at leading order near the wetting point, the quenched free energy has the same asymptotic behavior as the homogeneous free energy. In the homogeneous model, however, the free energy has a sequence of nondifferentiability points corresponding to first-order layering transitions between interfaces localized near consecutive integer heights.

The authors explain that disorder may round these transitions through the Aizenman–Wehr mechanism, but that the cited general result does not directly apply because the SOS height variable is unbounded. Establishing whether the homogeneous layering picture survives, or is replaced by rounded crossovers, therefore remains unresolved.