Geodesic
Conformal invariance in random cluster models. I. Holomorphic fermions in the Ising model
Stanislav Smirnov 1
1 Section de Mathématiques<br/>Université de Genève<br/>2-4, rue du Lièvre, c.p. 64<br/>CH-1211 Genève 4<br/>Switzerland
Annals of mathematics, Tome 172 (2010) no. 2, pp. 1435-1467 Cet article a éte moissonné depuis la source Annals of Mathematics website

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We construct discrete holomorphic fermions in the random cluster Ising model at criticality and show that they have conformally covariant scaling limits (as mesh of the lattice tends to zero). In the sequels those observables are used to construct conformally invariant scaling limits of interfaces and identify those with Schramm’s SLE curves. Though the critical Ising model is often cited as a classical example of conformal invariance, it seems that ours is the first paper where it is actually established.

DOI : 10.4007/annals.2010.172.1435

Stanislav Smirnov  1

1 Section de Mathématiques<br/>Université de Genève<br/>2-4, rue du Lièvre, c.p. 64<br/>CH-1211 Genève 4<br/>Switzerland 
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Stanislav Smirnov. Conformal invariance in random cluster models. I. Holomorphic fermions in the Ising model. Annals of mathematics, Tome 172 (2010) no. 2, pp. 1435-1467. doi: 10.4007/annals.2010.172.1435

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