Quenched random-mass disorder in the critical Gross-Neveu-Yukawa model

In the clean limit, continuous symmetry-breaking quantum phase transitions in 2D Dirac materials such as graphene and surfaces of 3D topological insulators are described by (2+1)D critical Gross-Neveu-Yukawa (GNY) models. In this talk, I will present recent results of the study of the effects of quenched random-mass disorder, both short- and long-range correlated, on the universal critical properties of the Ising, XY, and Heisenberg GNY models. The problem was studied via the application of the replica renormalization group combined with a controlled triple epsilon expansion below four dimensions. Among interesting results, we find new finite-disorder quantum critical and multicritical points and an instance of the supercritical Hopf bifurcation in the renormalization-group flow, which is accompanied by the birth of a stable limit cycle corresponding to discrete scale invariance.

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