Data and scripts from: Nontrivial critical fixed point for replica-symmetry-breaking transitions

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<d(u) using a two-loop calculation. Because the critical fixed point is found in the strong-coupling regime, we corroborate the result by resumming the perturbative series with inputs from a three-loop calculation and an analysis of its large-order behavior. Our study offers a resolution of the long-lasting controversy surrounding phase transitions in finite-dimensional disordered systems.

PLEASE NOTE: As of 06-06-2017, the data and scripts for Figure 2a, 2b, and 2c have been superseded subsequent to initial data publication.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)