  We introduce a formula for the disagreement function which is used to control
a recently proposed dynamics of the Ising spin system. This leads to four
different phases of the Ising spin chain in a zero temperature. One of these
phases is doubly degenerated (anti- and ferromagnetic states are equally
probable). On the borders between the phases two types of transitions are
observed: infinite degeneration and instability lines. The relaxation of the
system depends strongly on the phase.
