2 problems

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The Narayan–Middleton conjecture on charge-density waves and Abelian sandpiles
Let CDWs pinned by disorder undergo a depinning transition, and let the Abelian sandpile model be the corresponding sandpile model. Narayan–Middleton conjecture. CDWs pinned by dis…
Conjectureopenabelian-sandpile-models depinning statistical-physicsarXiv posted 2 days ago
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Conjecture on the Manhattan lattice filling number
Let $L$ be the side length of the square Manhattan lattice, and let $k_L$ denote its filling number. Filling-number conjecture. Based on extensive tests up to $L\simeq 100$ , the fi…
Conjectureopenabelian-sandpile-models lattice-modelsarXiv posted 2 days ago

The Narayan–Middleton conjecture on charge-density waves and Abelian sandpiles