The Blume-Capel model can be seen as a natural generalisation of the Ising model, where spins are allowed to take value in . In the first part of the talk, we will introduce the model, discuss its conjectural phase diagram, and state our main result concerning the existence of a tricritical point for the model on . In the second part of the talk, we present some of the main ideas of the proofs. In particular, we show how many beautiful probabilistic techniques developed over the last decades to study Ising and percolation models can be adapted to rigorously study various regimes of the Blume-Capel model and its phase transition.
Based on joint work with Trishen S. Gunaratnam (https://arxiv.org/abs/2210.13394).