  We investigate the effect of initial conditions on the dynamic exponents of
the interacting monomer-monomer model with infinitely many absorbing states in
one dimension. This model exhibits a directed Ising (DI) type transition from
an active phase into an absorbing phase. In case of the directed percolation
universality class, it has been reported that the non-order parameter as well
as the order parameter exhibits critical fluctuations, relaxing algebraically
to its natural value with the same scaling exponents. We numerically confirm
that this is also valid for the DI universality class. We also observe
continuously varying dynamic exponents with a linear dependence on the
non-order parameter initial density.
