We identify the scaling limit of full-plane Kadanoff–Ceva fermionson generic, non-degenerate s-embeddings. In this broad setting, the scaling limits are described in terms of solutions to conjugate Beltrami equations with prescribed singularities. For the underlying Ising model, this leads to the scaling limit of the energy–energy correlations connecting the scaling limits of (near-)critical planar Ising models to Green kernels of uniformly elliptic operators and quasiconformal mappings. For grids approximating bounded domains in the complex plane, we establish, in the scaling regime, the conformal covariance of the energy density on critical doubly periodic graph. Moreover, we prove a connection between the planar Ising energy field in smooth limiting strict and (massive)-holomorphic fermions defined on surfaces of the Minkowski space R^{(2,1)}. These results highlight that the scaling limits of generic (near-)critical Ising models naturally live on a substantially richer conformal structure than the classical Euclidean one.
