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

Publication ,  Journal Article
Charbonneau, P; Hu, Y; Raju, A; Sethna, JP; Yaida, S
Published in: Physical review. E
February 2019

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.

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Published In

Physical review. E

DOI

EISSN

2470-0053

ISSN

2470-0045

Publication Date

February 2019

Volume

99

Issue

2-1

Start / End Page

022132

Related Subject Headings

  • 51 Physical sciences
  • 49 Mathematical sciences
  • 40 Engineering
 

Citation

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Charbonneau, P., Hu, Y., Raju, A., Sethna, J. P., & Yaida, S. (2019). Morphology of renormalization-group flow for the de Almeida-Thouless-Gardner universality class. Physical Review. E, 99(2–1), 022132. https://doi.org/10.1103/physreve.99.022132
Charbonneau, Patrick, Yi Hu, Archishman Raju, James P. Sethna, and Sho Yaida. “Morphology of renormalization-group flow for the de Almeida-Thouless-Gardner universality class.Physical Review. E 99, no. 2–1 (February 2019): 022132. https://doi.org/10.1103/physreve.99.022132.
Charbonneau P, Hu Y, Raju A, Sethna JP, Yaida S. Morphology of renormalization-group flow for the de Almeida-Thouless-Gardner universality class. Physical review E. 2019 Feb;99(2–1):022132.
Charbonneau, Patrick, et al. “Morphology of renormalization-group flow for the de Almeida-Thouless-Gardner universality class.Physical Review. E, vol. 99, no. 2–1, Feb. 2019, p. 022132. Epmc, doi:10.1103/physreve.99.022132.
Charbonneau P, Hu Y, Raju A, Sethna JP, Yaida S. Morphology of renormalization-group flow for the de Almeida-Thouless-Gardner universality class. Physical review E. 2019 Feb;99(2–1):022132.

Published In

Physical review. E

DOI

EISSN

2470-0053

ISSN

2470-0045

Publication Date

February 2019

Volume

99

Issue

2-1

Start / End Page

022132

Related Subject Headings

  • 51 Physical sciences
  • 49 Mathematical sciences
  • 40 Engineering