  We update a one-dimensional chain of Ising spins of length $L$ with
algorithms which are parameterized by the probability $p$ for a certain site to
get updated in one time step. The result of the update event itself is
determined by the energy change due to the local change in the configuration.
In this way we interpolate between the Metropolis algorithm at zero temperature
for $p$ of the order of 1/L and for large $L$, and a synchronous deterministic
updating procedure for $p=1$. As function of $p$ we observe a phase transition
between the stationary states to which the algorithm drives the system. These
are non-absorbing stationary states with antiferromagnetic domains for $p>p_c$,
and absorbing states with ferromagnetic domains for $p\leq p_c$. This means
that above this transition the stationary states have lost any remnants to the
ferromagnetic Ising interaction. A measurement of the critical exponents shows
that this transition belongs to the universality class of parity conservation.
