Publications [#341867] of Patrick Charbonneau

Papers Published

1. Charbonneau, P; Hu, Y; Raju, A; Sethna, JP; Yaida, S, Morphology of renormalization-group flow for the de Almeida-Thouless-Gardner universality class., Physical review. E, vol. 99 no. 2-1 (February, 2019), pp. 022132 [doi]
   (last updated on 2024/04/23)

   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 (or limit cycle) may stay finite for all dimensions.