Journal
PHYSICAL REVIEW LETTERS
Volume 118, Issue 21, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevLett.118.215701
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Funding
- Simons Foundation [454937]
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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.
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