Phase transitions for $\phi^4_3$

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Trishen Gunaratnam
Université de Genève

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 magnetisation at sufficiently low temperatures in 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.