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The pair contact process with diffusion (PCPD) with modulo 2 conservation(\pcpdt) [$2A\to 4A$, $2A\to 0$] is studied in one dimension, focused on thecrossover to other well established universality classes: the directed Ising(DI) and the directed percolation (DP). First, we show that the \pcpdt sharesthe critical behaviors with the PCPD, both with and without directional bias.Second, the crossover from the \pcpdt to the DI is studied by including aparity-conserving single-particle process ($A \to 3A$). We find the crossoverexponent $1/\phi_1 = 0.57(3)$, which is argued to be identical to that of thePCPD-to-DP crossover by adding $A \to 2A$. This suggests that the PCPDuniversality class has a well defined fixed point distinct from the DP. Third,we study the crossover from a hybrid-type reaction-diffusion process belongingto the DP [$3A\to 5A$, $2A\to 0$] to the DI by adding $A \to 3A$. We find$1/\phi_2 = 0.73(4)$ for the DP-to-DI crossover. The inequality of $\phi_1$ and$\phi_2$ further supports the non-DP nature of the PCPD scaling. Finally, weintroduce a symmetry-breaking field in the dual spin language to study thecrossover from the \pcpdt to the DP. We find $1/\phi_3 = 1.23(10)$, which isassociated with a new independent route from the PCPD to the DP.

Crossover from the parity-conserving pair contact process with diffusion to other universality classes