Smirnov's convergence conjecture for the Potts parafermionic observable
Smirnov's convergence conjecture for the Potts parafermionic observable
Fix and . Let be Dobrushin domains approximating a simply connected domain with marked boundary points and , and let be the vertex parafermionic observable obtained by averaging the edge fermionic observable over neighboring edges. Let be the parameter used in the source, and let be a conformal map from to the strip mapping to and to . Smirnov's observable convergence conjecture.
The source explains that this convergence would imply the preceding conformal-invariance conjecture, but does not state that it has been proved in the full range .
Sources & referencesView supporting material
Primary source
Hugo Duminil-Copin, “Lectures on the Ising and Potts models on the hypercubic lattice”, arXiv:1707.00520 (2017).
Additional references
3 papers in this index state this conjecture (2012–2017). The statement above is taken from the most recent of them; the others are arXiv:1505.04159, arXiv:1208.3787.
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