  The persistent current in strictly one-dimensional Dirac systems is
investigated within two different models, defined in the continuum and on a
lattice, respectively. The object of the study is the effect of a single
magnetic or nonmagnetic impurity in the two systems. In the continuum Dirac
model, an analytical expression for the persistent current flowing along a ring
with a single delta-like magnetic impurity is obtained after regularization of
the unbounded negative energy states. The predicted decay of the persistent
agrees with the lattice simulations. The results are generalized to finite
temperatures. To realize a single Dirac massless fermion, the lattice model
breaks the time-reversal symmetry, and, in contrast with the continuum model, a
pointlike nonmagnetic impurity can lead to a decay in the persistent current.
