Nontrivial Critical Fixed Point for Replica-Symmetry-Breaking Transitions

Patrick Charbonneau and Sho Yaida
Phys. Rev. Lett. 118, 215701 – Published 26 May 2017
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Abstract

The transformation of the free-energy landscape from smooth to hierarchical is one of the richest features of mean-field disordered systems. A well-studied example is the de Almeida–Thouless transition for spin glasses in a magnetic field, and a similar phenomenon—the Gardner transition—has recently been predicted for structural glasses. The existence of these replica-symmetry-breaking phase transitions has, however, long been questioned below their upper critical dimension, du=6. Here, we obtain evidence for the existence of these transitions in d<du using a two-loop calculation. Because the critical fixed point is found in the strong-coupling regime, we corroborate the result by resumming the perturbative series with inputs from a three-loop calculation and an analysis of its large-order behavior. Our study offers a resolution of the long-lasting controversy surrounding phase transitions in finite-dimensional disordered systems.

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  • Received 18 July 2016

DOI:https://doi.org/10.1103/PhysRevLett.118.215701

© 2017 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied PhysicsStatistical Physics & Thermodynamics

Authors & Affiliations

Patrick Charbonneau1,2 and Sho Yaida1,*

  • 1Department of Chemistry, Duke University, Durham, North Carolina 27708, USA
  • 2Department of Physics, Duke University, Durham, North Carolina 27708, USA

  • *sho.yaida@duke.edu

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Issue

Vol. 118, Iss. 21 — 26 May 2017

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