Relaxation of non-order parameter field in directed Ising systems

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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.