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We introduce a novel random walk model that emerges in the event-chain MonteCarlo (ECMC) of spin systems. In the ECMC, the lifting variable specifying thespin 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 afeedback. We investigate this random walk numerically in the case of theclassical XY model in 1,2, and 3 dimensions to find that it is superdiffusivenear the critical point of the underlying spin system. It is suggested that theperformance improvement of the ECMC is related to this anomalous behavior.

Anomalous diffusion analysis of the lifting events in the event-chain Monte Carlo for the classical XY models