Random magnetic fields, supersymmetry, and negative dimensions

G. Parisi; N. Sourlas

doi:10.1103/PhysRevLett.43.744

Random magnetic fields, supersymmetry, and negative dimensions

G. Parisi^*
, N. Sourlas

^*Corresponding author for this work

National Institute for Nuclear Physics
École Normale Supérieure

Research output: Contribution to journal › Article › peer-review

808 Scopus citations

Abstract

We prove the equivalence, near the critical point, of a D-dimensional spin system in a random external magnetic field with a (D-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.

Original language	English
Pages (from-to)	744-745
Number of pages	2
Journal	Physical Review Letters
Volume	43
Issue number	11
DOIs	https://doi.org/10.1103/PhysRevLett.43.744
State	Published - 1979
Externally published	Yes

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10.1103/PhysRevLett.43.744

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AB - We prove the equivalence, near the critical point, of a D-dimensional spin system in a random external magnetic field with a (D-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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Random magnetic fields, supersymmetry, and negative dimensions

Abstract

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