Despite 40 years of works, the low temperature phase of Spin Glasses in finite dimension is still not understood. Indeed two theories, Full Replica Symmetry Breaking and Droplet Theory, have been proposed.The predictions of the two theories are completely different, both for spin glasses with or without field. By using real space renormalisation group (RG) methods we show that spin-glasses in a field display a new kind of transition in high dimensions. The corresponding critical properties and the spin-glass phase are governed by two non-perturbative zero temperature fixed points of the RG. We compute the critical exponents, discuss the RG flow and its relevance for three dimensional systems. The new spin-glass phase we discovered has unusual properties, which are intermediate between the ones conjectured by droplet and full replica symmetry breaking theories. These results provide a new perspective on the long-standing debate about the behaviour of spin-glasses in finite dimensions.

Sapienza, University of Rome, Department of Physics