Universality in the 2D Ising model and conformal invariance of fermionic observables

Understand

It is widely believed that the celebrated 2D Ising model at criticality has a universal and conformally invariant scaling limit, which is used in deriving many of its properties.

• However, no mathematical proof of universality and conformal invariance has ever been given, and even physics arguments support (a priori weaker) M\"obius invariance.
• We introduce discrete holomorphic fermions for the 2D Ising model at criticality on a large family of planar graphs.
• We show that on bounded domains with appropriate boundary conditions, those have universal and conformally invariant scaling limits, thus proving the universality and conformal invariance conjectures.