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

Slava Rychkov

doi:10.1007/978-3-031-42000-9

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arXiv · 2303.09654

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

Slava Rychkov

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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.

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Slava Rychkov. 2023-03-16. Four Lectures on the Random Field Ising Model, Parisi-Sourlas Supersymmetry, and Dimensional Reduction. https://doi.org/10.1007/978-3-031-42000-9

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