| Abstract: | Phase transitions in strongly correlated systems, especially those outside the Landau paradigm, pose various theoretical challenges. One of these is how to perform RG on strongly coupled microscopic Hamiltonians having discrete degrees of freedom. As a result field-theory approaches often become disconnected from the microscopics. Such is the case in two critical models we discuss in this talk - the self-dual Ising Higgs gauge transition in 3D and a critical phase of dimer models on the Ammann-Beenker tiling. Leveraging recent connections between information theory and RG, we perform extensive deep-learning-based data analysis on Monte-Carlo snapshots of these critical phases. Using those we are able to support and substantiate an existing conjecture regarding the above dimer model and largely refute the claim that the self-dual Ising Higgs transition is of the XY* type. |