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A nontrivial critical fixed point for replica-symmetry-breaking transitions

Date
2017-04-01
Authors
Charbonneau, Patrick
Yaida, Sho
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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, d_u=6. Here, we obtain evidence for the existence of these transitions in d<d_u 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. Our analysis offers a straightforward resolution of the long-lasting controversy surrounding phase transitions in finite-dimensional disordered systems.
Type
Journal article
Subject
cond-mat.stat-mech
cond-mat.stat-mech
cond-mat.dis-nn
hep-th
Permalink
https://hdl.handle.net/10161/13923
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Scholars@Duke

Charbonneau

Patrick Charbonneau

Professor of Chemistry
Professor Charbonneau studies soft matter. His work combines theory and simulation to understand the glass problem, protein crystallization, microphase formation, and colloidal assembly in external fields.

Sho Yaida

Postdoctoral Associate
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