  We study the disorder-induced phase transition of higher-order Weyl
semimetals (HOWSMs) and the fate of the topological features of disordered
HOWSMs. We obtain a global phase diagram of HOWSMs according to the scaling
theory of Anderson localization. Specifically, a phase transition from the Weyl
semimetal (WSM) to the HOWSM is uncovered, distinguishing the disordered HOWSMs
from the traditional WSMs. Further, we confirm the robustness of Weyl-nodes for
HOWSMs. Interestingly, the unique topological properties of HOWSMs show
different behaviors: (i) the quantized quadrupole moment and the corresponding
quantized charge of hinge states are fragile to weak disorder; (ii) the hinge
states show moderate stability which enables the feasibility in experimental
observation. Our study deepens the understanding of the topological nature of
HOWSMs and paves a possible way to the characterization of such a phase in
experiments.
