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It is widely believed that the celebrated 2D Ising model at criticality has auniversal and conformally invariant scaling limit, which is used in derivingmany of its properties. However, no mathematical proof of universality andconformal invariance has ever been given, and even physics arguments support (apriori weaker) M\"obius invariance. We introduce discrete holomorphic fermionsfor the 2D Ising model at criticality on a large family of planar graphs. Weshow that on bounded domains with appropriate boundary conditions, those haveuniversal and conformally invariant scaling limits, thus proving theuniversality and conformal invariance conjectures.

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