Nontrivial critical fixed point for replica-symmetry-breaking transitions

TL;DR

This paper provides evidence for the existence of replica-symmetry-breaking phase transitions in finite-dimensional disordered systems below six dimensions, resolving a long-standing controversy through advanced perturbative calculations.

Contribution

It demonstrates the existence of a nontrivial critical fixed point for RSB transitions in dimensions less than six using two-loop and three-loop calculations, and series resummation.

Findings

Evidence for RSB transitions in d<6 from two-loop calculations.

Resummation confirms the strong-coupling fixed point.

Resolves controversy over phase transitions in finite-dimensional disordered systems.

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.