A nontrivial critical fixed point for replica-symmetry-breaking transitions
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 articlePermalink
https://hdl.handle.net/10161/13923Collections
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Show full item recordScholars@Duke
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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