English

Conformal invariance in random cluster models. I. Holomorphic fermions in the Ising model

Mathematical Physics 2009-09-30 v1 math.MP Probability

Abstract

We construct discrete holomorphic observables in the Ising model at criticality and show that they have conformally covariant scaling limits (as mesh of the lattice tends to zero). In the sequel those observables are used to construct conformally invariant scaling limits of interfaces. Though 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.

Keywords

Cite

@article{arxiv.0708.0039,
  title  = {Conformal invariance in random cluster models. I. Holomorphic fermions in the Ising model},
  author = {Stanislav Smirnov},
  journal= {arXiv preprint arXiv:0708.0039},
  year   = {2009}
}
R2 v1 2026-06-21T09:03:41.661Z