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

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arxiv 2303.09654 v2 pith:TBNTBJSW submitted 2023-03-16 cond-mat.stat-mech cond-mat.dis-nnhep-thmath-phmath.MP

classification cond-mat.stat-mechcond-mat.dis-nnhep-thmath-phmath.MP
keywords modeldimensionalfieldisinglecturesparisi-sourlasrandomreduction
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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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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Ising surface defects can get dirty

    hep-th 2026-05 unverdicted novelty 7.0 of 10

    Replica one-loop RG of Wilson-Fisher theory with surface random field yields a mixed-stable dirty defect fixed point and logarithmic multiplets in the N o0 limit.

  2. Critical dynamics of a scalar field near four spatial dimensions

    hep-th 2026-08 accept novelty 6.0 of 10

    The exactly dissipationless critical dynamics of a scalar field is an invariant but unstable surface of the RG flow, and any small friction drives it to Model A, with new two-loop dynamic exponents.

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