Problem dossier · Algorithms & Simulation
Self-avoiding walks
Count self-avoiding walks of length n on a lattice and pin down the connective constant μ and critical exponents. On Z² the constant is unknown (≈ 2.638).
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Status
Open on the square lattice; solved exactly on the honeycomb lattice (μ = √(2+√2), Duminil-Copin–Smirnov 2010). Exponent conjectures (11/32) rest on conformal-invariance predictions.
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The Angle of Attack
Extend series enumeration with transfer-matrix / finite-lattice methods; Monte Carlo (pivot algorithm) at scale to sharpen μ and exponent estimates.
Tags: lattice · enumeration · monte carlo · critical exponents
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The Lab
No instruments built yet. When this problem gets tackled, its interactive instruments — explorers, searches, verifiers running in the browser — live here. See the Collatz dossier for what a fully tackled problem looks like.
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The Log
Empty. Work on this problem gets logged here as dated entries — constructions tried, code run, dead ends included. Dead ends are results.
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