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Résumé |
Quenched disorder is very important but notoriously hard. In 1979, Parisi and
Sourlas proposed an interesting and powerful conjecture about the infrared fixed
points with random field (RF) type of disorder: such fixed points should possess
an unusual supersymmetry, by which they reduce in two less spatial dimensions to
usual non-supersymmetric non-disordered fixed points. The conjecture is known to
hold for the RF phi^3 model but not for RF phi^4 model in d < 5 dimensions,
however there is no consensus on why this happens. We argue that: 1) dimensional
reduction works for any Parisi-Sourlas SUSY fixed point; 2) the SUSY fixed point
is not always reached because of relevant SUSY-breaking interactions. We attack
the point 1) using axiomatic CFT techniques while we study the point 2) using the
perturbative renormalization group in a judiciously chosen field basis, allowing
systematic exploration of the space of interactions. Our computations agree with
the numerical results for both cubic and quartic potential. |
