Fifth seminar of the Series "The interdisciplinary contribution of Giorgio Parisi to theoretical physics". Supersymmetry is a symmetry between bosonic and fermionic fields, popular in conjectural extensions of the Standard Model of particle physics. But Parisi and Sourlas pointed out in 1979 that statistical physicists should also be interested in it. They showed how supersymmetry may be an emergent symmetry of the phase transition of the Ising model coupled to a random magnetic field. Furthermore, they showed that supersymmetry implies dimensional reduction of critical exponents: exponents of the random field Ising model in D dimensions should be those of the ordinary Ising model in D-2 dimensions. We will discuss the original insights, as well as the more recent numerical simulations and theoretical work suggesting that Parisi-Sourlas supersymmetry is present in the random Ising model in 5 dimensions and above, and in any D in a related model describing branched polymers.
M.C.Angelini, M.Bonvini, G.Gradenigo, R.Aloisio, A.D.Polosa, F.Ricci-Tersenghi