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Supersymmetry and its spontaneous breaking in the random field Ising model

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arxiv 1103.4812 v2 pith:WSOC6QZA submitted 2011-03-24 cond-mat.stat-mech

Matthieu Tissier , Gilles Tarjus This is my paper · ORCID
classification cond-mat.stat-mech
keywords breakingcriticaldimensionexponentsfieldisingmodelrandom
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abstract

We provide a resolution of one of the long-standing puzzles in the theory of disordered systems. By reformulating the functional renormalization group (FRG) for the critical behavior of the random field Ising model in a superfield formalism, we are able to follow the associated supersymmetry and its spontaneous breaking along the FRG flow. Breaking is shown to occur below a critical dimension $d_{DR}\simeq 5.1$ and leads to a breakdown of the "dimensional reduction" property. We compute the critical exponents as a function of dimension and give evidence that scaling is described by three independent exponents.

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  1. Parisi-Sourlas Supertranslation and Scale without Conformal symmetry

    hep-th 2024-11 accept novelty 7.0 of 10

    Supertranslation symmetry protects the virial current's scaling dimension, giving eight perturbative scale-invariant but non-conformal fixed points in a quartic superfield model.

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