Morphology of renormalization-group flow for the de Almeida-Thouless-Gardner universality class.
Published
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
Pubmed Central 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
Language
- eng