Supersymmetry and its spontaneous breaking in the random field Ising model

Details Supersymmetry and its spontaneous breaking in the random field Ising model Supersymmetry and its spontaneous breaking in the random field Ising model

2011-03-24

arxiv.org/abs/1103.4812v2

Phys. Rev. Lett. 107, 041601 (2011)

Physics

Condensed Matter

Statistical Mechanics

4 pages, 2 figures

Scientific paper

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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