Morphology of renormalization-group flow for the de Almeida-Thouless-Gardner universality class
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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 articlePermalink
https://hdl.handle.net/10161/17391Collections
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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.

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