On controlling simple dynamics by a disagreement function

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 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.