Random Magnetic Fields, Supersymmetry and Negative Dimensions

Parisi, G.; Sourlas, N.

doi:10.1103/PhysRevLett.43.744

Random Magnetic Fields, Supersymmetry and Negative Dimensions

G. Parisi
(
- Frascati
)
,
N. Sourlas
(
- Ecole Normale Superieure
)

Jun, 1979

7 pages

Published in:

Phys.Rev.Lett. 43 (1979) 744

DOI:

10.1103/PhysRevLett.43.744

Report number:

LPTENS-79-13

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Abstract: (APS)

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.

MODEL: SPIN
SPIN: MODEL
MAGNETIC FIELD: EXTERNAL FIELD
SUPERSYMMETRY
DIFFERENTIAL EQUATIONS: STOCHASTIC

References(13)

Figures(0)

Random-Field Instability of the Ordered State of Continuous Symmetry

Yoseph Imry
(
- Brookhaven
)
,
Shang-keng Ma
(
- UC, San Diego
)

- Phys.Rev.Lett. 35 (1975) 1399-1401
•
DOI:
- 10.1103/PhysRevLett.35.1399

- J.Phys.C 10 L257

Supersymmetry

- Phys.Rept. 32 (1977) 249-334
•
DOI:
- 10.1016/0370-1573(77)90066-7

Theory of spin glasses

- J.Phys.F 5 (1975) 5, 965
•
DOI:
- 10.1088/0305-4608/5/5/017

Statistical Dynamics of Classical Systems

P.C. Martin
(
- Harvard U. and
- Orsay and
- SPhN, DAPNIA, Saclay
)
,
E.D. Siggia
(
- Harvard U. and
- Orsay and
- SPhN, DAPNIA, Saclay
)
,
H.A. Rose
(
- Harvard U.
)

- Phys.Rev.A 8 (1973) 423-437
•
DOI:
- 10.1103/PhysRevA.8.423

Renormalization-group methods for critical dynamics: 1. Recursion relations and effects of energy conservation

B.I. Halperin
(
- Bell Labs
)
,
P.C. Hohenberg
(
- Bell Labs
)
,
Shang-keng Ma
(
- UC, San Diego and
- UC, Berkeley
)

- Phys.Rev.B 10 (1974) 139-153
•
DOI:
- 10.1103/PhysRevB.10.139

Renormalization of Gauge Theories

- Annals Phys. 98 (1976) 287-321,
- Also in *Lai, C. H. (ed.): Gauge Theory Of Weak and Electromagnetic Interactions*, 416-450
•
DOI:
- 10.1016/0003-4916(76)90156-1

Lowest order divergent graphs in nu-dimensional space

C.G. Bollini
(
- La Plata U.
)
,
J.J. Giambiagi
(
- La Plata U.
)

- Phys.Lett.B 40 (1972) 566-568
•
DOI:
- 10.1016/0370-2693(72)90483-2

Critical exponents in 3.99 dimensions

- Phys.Rev.Lett. 28 (1972) 240-243
•
DOI:
- 10.1103/PhysRevLett.28.240

Regularization and Renormalization of Gauge Fields

Gerard 't Hooft
(
- Utrecht U.
)
,
M.J.G. Veltman
(
- Utrecht U.
)

- Nucl.Phys.B 44 (1972) 189-213,
- Also in *Lai, C. H. ( Ed.): Gauge Theory Of Weak and Electromagnetic Interactions*, 322-346
•
DOI:
- 10.1016/0550-3213(72)90279-9

Supergauge Transformations

Abdus Salam
(
- ICTP, Trieste and
- Imperial Coll., London
)
,
J.A. Strathdee
(
- ICTP, Trieste
)

- Nucl.Phys.B 76 (1974) 477-482,
- Also in *Ferrara, S. (ed.): Supersymmetry, vol. 1* 35-40,
- Also in *Salam, A. (ed.), Sezgin, E. (ed.): Supergravities in diverse dimensions, vol. 1* 36-41,
- Also in *Ali, A. (ed.) et al.: Selected papers of Abdus Salam* 404-409
•
DOI:
- 10.1016/0550-3213(74)90537-9

Feynman Rules for Superfields

Abdus Salam
(
- ICTP, Trieste and
- Imperial Coll., London
)
,
J.A. Strathdee
(
- ICTP, Trieste
)

- Nucl.Phys.B 86 (1975) 142-152
•
DOI:
- 10.1016/0550-3213(75)90078-4

Superfield Perturbation Theory and Renormalization

Robert Delbourgo
(
- Imperial Coll., London
)

- Nuovo Cim.A 25 (1975) 646
•
DOI:
- 10.1007/BF02729305