Random Magnetic Fields, Supersymmetry, and Negative Dimensions

  title={Random Magnetic Fields, Supersymmetry, and Negative Dimensions},
  author={G. Parisi and N. Sourlas},
  journal={Physical Review Letters},
  • G. Parisi, N. Sourlas
  • Published 1979
  • Physics
  • Physical Review Letters
  • We prove the equivalence, near the critical point, of a $D$-dimensional spin system in a random external magnetic field with a ($D\ensuremath{-}2$)-dimensional spin system in the absence of a magnetic field. This is due to the hidden supersymmetry of the associated stochastic differential equation. We identify a space with one anticommuting coordinate with a space having negative dimensions -2. 
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