Strong randomness criticality in the scratched-XY model

We study the finite-temperature superfluid--normal-liquid classical phase transitions in a disordered two-dimensional XY model with power law distributed "scratch"-like bond disorder. While for weak disorder the transition is of Berezinskii-Kosterlitz-Thouless type, the transition in the strong disorder regime is in a different universality class with a non-universal jump of the superfluid stiffness. We show this new criticality can be described by the asymptotically exact theory of superfluid-insulator quantum phase transition in one-dimensional disordered boson systems and discuss possible experimental realizations.