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(14:00-15:00 UTC) Speaker: Hendrik Weber (University of Bath)

Title: Phase transitions for $\phi^4_3$ - Part 1

Abstract: The $\phi^4$ model is a classical model in Mathematical Physics, arising e.g. as a continuous version of the Ising model, as a toy model for a Quantum field theory and it is also closely related to the invariant measures of certain Hamiltonian PDEs. The aim of this series of two talks is to discuss the infinite volume limit and the emergence of phase transitions for this model:
we will show that in a certain parameter regime, the model exhibits a phase segregation behaviour, akin to the low temperature phase of the Ising model.
In the first lecture I will put our result into perspective by first discussing the connection of continuous $\phi^4$ and discrete Ising models as well as the phase segregation in low temperature Ising models. I will then discuss a variational approach to estimating the $\phi^4$ partition function, which is due to Barashkov and Gubinelli and a key ingredient of our method.
Based on Chandra, Gunaratnam, Weber, arXiv:2006.15933.

(15:00-16:00 UTC) Speaker: Trish Gunaratnam (University of Geneva)
Title: Phase transitions for $\phi^4_3$ - Part 2
Abstract: In this talk I will continue to discuss phase transitions for $\phi^4_3$. I will establish a surface order large deviations estimate for the average magnetisation at sufficiently low temperatures in large but finite volumes.
This immediately gives an upper bound on the decay of the spectral gap for the associated $\phi^4_3$ singular SPDE in the infinite volume limit. At the heart of this result are the development of Peierls’ contour bounds for $phi^4_3$, which requires control over the small-scale divergences and the low temperature Hamiltonian. We achieve this by incorporating a low temperature expansion, inspired by Glimm, Jaffe, and Spencer’s classical work on $\phi^4_2$, within the variational representation of the $\phi^4_3$ via coarse-graining.
Based on Chandra, Gunaratnam, Weber, arXiv:2006.15933.

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