The critical phenomena of the Blume-Capel model

The Blume-Capel model is a generalisation of the Ising model where spins are allowed to also take the value 0 (i.e. vacant). It has received significant interest in the physics literature due to its exotic critical behaviour. There is a curve of critical points that govern the model's magnetisation-demagnetisation phase transition. Along this critical curve, the model has a further critical point which marks the threshold between continuous critical and discontinuous critical behaviour: the tricritical point. In the first part of the talk, I will introduce this model and describe its (tri)critical phenomena. It should accessible to all. In the second part of the talk, I will discuss a joint work with Dmitry Krachun (Princeton University) and Christoforos Panagiotis (University of Bath) where we show the existence of a tricritical point in all dimensions, and explain some ideas of the proof.