Morphology of renormalization-group flow for the de Almeida-Thouless-Gardner universality class.

Journal Article (Journal Article)

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 strong-coupling fixed point (or limit cycle) may stay finite for all dimensions.

Full Text

Duke Authors

Cited Authors

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

Published Date

  • February 2019

Published In

Volume / Issue

  • 99 / 2-1

Start / End Page

  • 022132 -

PubMed ID

  • 30934357

Electronic International Standard Serial Number (EISSN)

  • 2470-0053

International Standard Serial Number (ISSN)

  • 2470-0045

Digital Object Identifier (DOI)

  • 10.1103/physreve.99.022132


  • eng