  We introduce a novel random walk model that emerges in the event-chain Monte
Carlo (ECMC) of spin systems. In the ECMC, the lifting variable specifying the
spin to be updated changes its value to one of its interacting neighbor spins.
This movement can be regarded as a random walk in a random environment with a
feedback. We investigate this random walk numerically in the case of the
classical XY model in 1,2, and 3 dimensions to find that it is superdiffusive
near the critical point of the underlying spin system. It is suggested that the
performance improvement of the ECMC is related to this anomalous behavior.
