Controlling simple dynamics by a disagreement function

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Abstract
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 at zero temperature. One of these phases is doubly degenerated (antiferromagnetic 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.
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