One-arm exponents of the high-dimensional Ising model

In joint work with Diederik van Engelenburg, Romain Panis and Franco Severo, we study the probability that the origin is connected to the boundary of the box of size n (the one-arm probability) in several percolation models related to the Ising model. We prove that different universality classes emerge at criticality and that the FK-Ising model has upper-critical dimension equal to 6, in contrast to the Ising model where it is known to be equal to (or less than) 4. I will start the talk with a short introduction on the Ising model on Z^d.