  In systems with frustration, the critical slowdown of the dynamics severely
impedes the numerical study of phase transitions for even the simplest of
lattice models. In order to help sidestep the gelation-like sluggishness, a
clearer understanding of the underlying physics is needed. Here, we first
obtain generic insights into that phenomenon by studying one-dimensional and
Bethe lattice versions of a schematic frustrated model, the axial next-nearest
neighbor Ising (ANNNI) model. Based on these findings, we formulate two cluster
algorithms that speed up the simulations of the ANNNI model on a 2D square
lattice. Although these schemes do not avoid the critical slowdown, speed-ups
of factors up to 40 are achieved in some regimes.
