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Planar Ising model at criticality: state-of-the-art and perspectives
In this essay, we briefly discuss recent developments, started a decade ago
in the seminal work of Smirnov and continued by a number of authors, centered
around the conformal invariance of the critical planar Ising model on
and, more generally, of the critical Z-invariant Ising model on
isoradial graphs (rhombic lattices). We also introduce a new class of
embeddings of general weighted planar graphs (s-embeddings), which might, in
particular, pave the way to true universality results for the planar Ising
model.Comment: 19 pages (+ references), prepared for the Proceedings of ICM2018.
Second version: two references added, a few misprints fixe
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