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

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  • 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. ... [Read More]

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63 files (1.78 MB)
Data Citation
  • Charbonneau, P., Hu, Y., Raju, A., Sethna, J., & Yaida, S. (2019). Data and scripts from: Morphology of renormalization-group flow for the de Almeida–Thouless–Gardner universality class. Duke Digital Repository. https://doi.org/10.7924/r4zc7wm7d
DOI
  • 10.7924/r4zc7wm7d
Publication Date
ARK
  • ark:/87924/r4zc7wm7d
Type
Related Materials
Funding Agency
  • Simons Foundation
  • National Science Foundation
Grant Number
  • National Science Foundation Grant No. NSF DMR-1719490
  • Simons Foundation Grant No. 454937
Contact
Title
  • Data and scripts from: Morphology of renormalization-group flow for the de Almeida–Thouless–Gardner universality class

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