Abstract
In this talk I will discuss recent results obtained in joint work with Ajay Chandra (Imperial) and Hendrik Weber (Bath) about the large-scale behaviour of the $\phi^4_3$ Euclidean field theory. In particular, I will discuss a surface order large deviations estimate for the average magnetisationat sufficiently low temperaturesin large but finite volumes. This is a manifestation of phase transition, which is well-known for this model. As a byproduct of this, one can quantify a breakdown of ergodicity for the Glauber dynamics of this model – given by the dynamical $\phi^4_3$ singular SPDE – for sufficiently low temperatures in the infinite volume limit.