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One-dimensional non-equilibrium kinetic Ising models evolving under thecompeting effect of spin flips at zero temperature and nearest-neighbour spinexchanges exhibiting directed percolation-like parity conserving(PC) phasetransition on the level of kinks are now further investigated, numerically,from the point of view of the underlying spin system. Critical exponentscharacterising its statics and dynamics are reported. It is found that theinfluence of the PC transition on the critical exponents of the spins is strongand the origin of drastic changes as compared to the Glauber-Ising case can betraced back to the hyperscaling law stemming from directed percolation(DP).Effect of an external magnetic field, leading to DP-type critical behaviour onthe level of kinks, is also studied, mainly through the generalised mean fieldapproximation.Comment: 15 pages, using RevTeX, 13 Postscript figures included, submitted to  J.Phys.A, figures 12 and 13 fixe

Phase transitions and critical behaviour in one-dimensional non-equilibrium kinetic Ising models with branching annihilating random walk of kinks