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Title: Can random disorder localize an interacting system in two dimensions
Plain: In two dimensions, rare regions with weak disorder are argued to grow and thermalize their surroundings. Whether that argument holds is not settled.
Precise: 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.
Settled by: 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.
Kind: well-posed
Answer type: yes-no
References: (empty)
Literature status: contested
Status 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).
Posed since: 2017