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Scaling nature of absorbing critical phenomena is well understood for thedirected percolation (DP) and the directed Ising (DI) systems. However, a fullanalysis of the crossover behavior is still lacking, which is of our interestin this study. There are three different routes from the DI to the DP classesby introducing a symmetry breaking field (SB), breaking a modulo 2 conservation(CB), or making channels connecting two equivalent absorbing states (CC). Eachroute can be characterized by a crossover exponent, which is found numericallyas $\phi=2.1\pm 0.1$ (SB), $4.6\pm 0.2$ (CB), and $2.9\pm 0.1$ (CC),respectively. The difference between the SB and CB crossover can be understoodeasily in the domain wall language, while the CC crossover involves anadditional critical singularity in the auxiliary field density with the memoryeffect to identify itself independent.

Three different routes from the directed Ising to the directed percolation class