Nontrivial critical fixed point for replica-symmetry-breaking transitions
arXiv:1607.04217 · doi:10.1103/PhysRevLett.118.215701
Abstract
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.
4+18 pages, 2+3 figures; v3: final version, with an analysis of large-order behavior added. Data relevant to this work can be accessed at http://dx.doi.org/10.7924/G86Q1V5C
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