The transformation of the free-energy landscape from smooth to hierarchical is one of the richest features of mean-field disordered systems. A well-studied example is the de Almeida–Thouless transition for spin glasses in a magnetic field and a similar phenomenon--the Gardner transition--has recently been predicted for structural glasses. The existence of these replica-symmetry-breaking phase transitions has however long been questioned below their upper critical dimension d(u)=6. Here we obtain evidence for the existence of these transitions in d PLEASE NOTE: As of 06-06-2017 the data and scripts for Figure 2a 2b and 2c have been superseded subsequent to initial data publication. Revised data and scripts are noted as such and represent the most current version of the data that should be used to replicate the findings presented within the Physical Review Letters article (118 215701)
