Conformal invariance of spin correlations in the planar Ising model. (English) Zbl 1318.82006
Summary: We rigorously prove the existence and the conformal invariance of scaling limits of the magnetization and multi-point spin correlations in the critical Ising model on arbitrary simply connected planar domains. This solves a number of conjectures coming from the physical and the mathematical literature. The proof relies on convergence results for discrete holomorphic spinor observables and probabilistic techniques.
MSC:
| 82B20 | Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics |
| 82D40 | Statistical mechanics of magnetic materials |
| 82B27 | Critical phenomena in equilibrium statistical mechanics |
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