Four Lectures on the Random Field Ising Model, Parisi-Sourlas Supersymmetry, and Dimensional Reduction


Numerical evidence suggests that the Random Field Ising Model loses Parisi-Sourlas SUSY and the dimensional reduction property somewhere between 4 and 5 dimensions, while a related model of branched polymers retains these features in any dd. These notes give a leisurely introduction to a recent theory, developed jointly with A. Kaviraj and E. Trevisani, which aims to explain these facts. Based on the lectures given in Cortona and at the IHES in 2022.Comment: 55 pages, 11 figures; v2 - minor changes, mentioned forthcoming work by Fytas et a

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