We prove universality of spin correlations in the scaling limit of the planar Ising model on isoradial graphs and Z–invariant weights. Specifically, we show that in the massive scaling limit, (i. e. as the mesh size tends to zero at the same rate as the inverse temperature goes to the critical one) the two-point spin correlations converges to a rotationally invariant function, which is universal among isoradial graphs and independant of the local geometry. We also give a simple proof of the fact that the infinite-volume sub-critical magnetization is independent of the site and the local geometry of the lattice. Finally, we provide a geometrical interpretation of the correlation length using the formalism of s-embeddings introduced recently by Chelkak.
Based on a joint work (arXiv:2104.12858) with Dmitry Chelkak (ENS), Konstantin Izyurov (Helsinki).