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

Abstract

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 $d$. 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.

55 pages, 11 figures; v2 - minor changes, mentioned forthcoming work by Fytas et al

Cited by in corpus (4)

• The Parisi-Sourlas Uplift and Infinitely Many Solvable 4d CFTs
• On the breakdown of dimensional reduction and supersymmetry in random-field models
• Crumpled-to-flat transition of quenched disordered membranes at two-loop order
• Topological Field Theory and Stochastic Dynamics