  We consider two-dimensional (2D) Dirac quantum ring systems formed by the
infinite mass constraint. When an Aharonov-Bohm magnetic flux is present, e.g.,
through the center of the ring domain, persistent currents, i.e., permanent
currents without dissipation, can arise. In real materials, impurities and
defects are inevitable, raising the issue of robustness of the persistent
currents. Using localized random potential to simulate the disorders, we
investigate how the ensemble averaged current magnitude varies with the
disorder density. For comparison, we study the nonrelativistic quantum
counterpart by analyzing the solutions of the Schr\"{o}dinger equation under
the same geometrical and disorder settings. We find that, for the Dirac ring
system, as the disorder density is systematically increased, the average
current decreases slowly initially and then plateaus at a finite nonzero value,
indicating remarkable robustness of the persistent currents. The physical
mechanism responsible for the robustness is the emergence of a class of
boundary states - whispering gallery modes. In contrast, in the Schr\"{o}dinger
ring system, such boundary states cannot form and the currents diminish rapidly
to zero with increase in the disorder density. We develop a physical theory
based on a quasi one-dimensional approximation to understand the striking
contrast in the behaviors of the persistent currents in the Dirac and
Schr\"{o}dinger rings. Our 2D Dirac ring systems with disorders can be
experimentally realized, e.g., on the surface of a topological insulator with
natural or deliberately added impurities from the fabrication process.
