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

Charbonneau, Patrick

Hu, Yi

Raju, Archishman

Sethna, James P

Yaida, Sho

2018-09-07T15:10:01Z

2018-09-07T15:10:01Z

2018-09-07T15:10:00Z

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.

https://hdl.handle.net/10161/17391

American Physical Society (APS)

cond-mat.stat-mech

cond-mat.stat-mech

cond-mat.dis-nn

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

Journal article

Charbonneau, Patrick|0000-0001-7174-0821

Trinity College of Arts & Sciences

Duke

Chemistry

Physics