Spin Glass in a Field: a New Zero-Temperature Fixed Point in Finite Dimensions

Abstract: 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 flow. 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 a field.