Can random disorder localize an interacting system in two dimensions
In plain words
In two dimensions, rare regions with weak disorder are argued to grow and thermalize their surroundings. Whether that argument holds is not settled.
Precise statement
For interacting lattice models in $d=2$ with independent random on-site disorder (e.g. hard-core bosons with nearest-neighbour hopping and disorder of width $W$), does any finite $W$ give infinite-time localization of local observables as $L\to \infty$? The avalanche argument of De Roeck and Huveneers (2017) predicts no. Answer yes or no.
What would settle it
Experiments or numerics showing whether the apparent localization crossover $W*(L)$ keeps drifting upward with $L$ up to sizes where a thermal region of the predicted critical size is typical.
Status in the literature
Unverified note
A 2025 optical-lattice study up to 24 x 24 sites reported the random-disorder crossover drifting to higher W with system size, consistent with avalanches (identifier not verified).