Data and scripts from: Morphology of renormalization-group flow for the de Almeida–Thouless–Gardner universality class


A replica-symmetry-breaking phase transition is predicted in a host of disordered media. The criticality of the transition has, however, long been questioned below its upper critical dimension, six, due to the absence of a critical fixed point in the renormalization-group flows at one-loop order. A recent two-loop analysis revealed a possible strong-coupling fixed point, but given the uncontrolled nature of perturbative analysis in the strong- coupling regime, debate persists. Here we examine the nature of the transition as a function of spatial dimension and show that the strong-coupling fixed point can go through a Hopf bifurcation, resulting in a critical limit cycle and a concomitant discrete scale invariance. We further investigate a different renormalization scheme and argue that the basin of attraction of the limit cycle at the strong-coupling fixed point may stay finite for all dimensions.

Data Access

Duke Authors

Cited Authors

  • Charbonneau, P; Yaida, S; Sethna, JP; Raju, A; Hu, Y

Published Date

  • February 13, 2019

Digital Object Identifier (DOI)

  • 10.7924/r4zc7wm7d