Real Space Migdal–Kadanoff Renormalisation of Glassy Systems: Recent Results and a Critical Assessment
In this manuscript, in honour of L. Kadanoff, we present recent progress obtained in the description of finite dimensional glassy systems thanks to the Migdal–Kadanoff renormalisation group (MK-RG). We provide a critical assessment of the method, in particular discuss its limitation in describing situations in which an infinite number of pure states might be present, and analyse the MK-RG flow in the limit of infinite dimensions. MK-RG predicts that the spin-glass transition in a field and the glass transition are governed by zero-temperature fixed points of the renormalization group flow.