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

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Authors
Charbonneau, Patrick
Hu, Yi
Raju, Archishman
Sethna, James P
Yaida, Sho
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Abstract
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/limit cycle may thus stay finite for all dimensions.
Type
Journal article
Subject
cond-mat.stat-mech
cond-mat.stat-mech
cond-mat.dis-nn
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https://hdl.handle.net/10161/17391
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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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