  We analyze large deviations of the time-averaged activity in the one
dimensional Fredrickson-Andersen model, both numerically and analytically. The
model exhibits a dynamical phase transition, which appears as a singularity in
the large deviation function. We analyze the finite-size scaling of this phase
transition numerically, by generalizing an existing cloning algorithm to
include a multi-canonical feedback control: this significantly improves the
computational efficiency. Motivated by these numerical results, we formulate an
effective theory for the model in the vicinity of the phase transition, which
accounts quantitatively for the observed behavior. We discuss potential
applications of the numerical method and the effective theory in a range of
more general contexts.
