Compact parity conserving percolation in one-dimension

Compact directed percolation is known to appear at the endpoint of the directed percolation critical line of the Domany-Kinzel cellular automaton in 1+1 dimension. Equivalently, such transition occurs at zero temperature in a magnetic field in the Glauber-Ising model and is shown to transform into compact parity conserving percolation transition under the effect of the critical fluctuations at the parity-conserving phase transition in the framework of the one-dimensional non-equilibrium kinetic Ising model. The characteristic exponents of spreading are found by numerical simulations, they differ from their compact directed percolation counterparts while the hyperscaling relation holds in its form appropriate for compact directed percolation.