Nontrivial Critical Fixed Point for Replica-Symmetry-Breaking Transitions.

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2017-05-26

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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 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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Published Version (Please cite this version)

10.1103/PhysRevLett.118.215701

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Charbonneau, Patrick, and Sho Yaida (2017). Nontrivial Critical Fixed Point for Replica-Symmetry-Breaking Transitions. Phys Rev Lett, 118(21). p. 215701. 10.1103/PhysRevLett.118.215701 Retrieved from https://hdl.handle.net/10161/15346.

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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.


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