  We study the critical phenomena of viable clusters in multiplex
two-dimensional lattices using numerical simulations. We identify viable sites
on multiplex lattices using two cascading algorithms: the cascade of
activations (CA) and deactivations (CD). We found that the giant viable
clusters identified by CA and CD processes exhibit different critical
behaviors. Specifically, the critical phenomena of CA processes are consistent
with the ordinary bond percolation on a single layer but CD processes exhibit
the critical behaviors consistent with mutual percolation on multiplex
lattices. In addition, we computed the susceptibility of cascading dynamics by
using the concept of ghost field. Our results suggest that the CA and CD
processes generate viable clusters in different ways.
