On controlling simple dynamics by a disagreement function

TL;DR

This paper introduces a disagreement function to control Ising spin dynamics, revealing four phases at zero temperature, with phase transitions and varied relaxation behaviors.

Contribution

It presents a novel disagreement function for controlling Ising spin dynamics and characterizes four distinct phases at zero temperature.

Findings

Four phases of the Ising spin chain identified.

Phase transitions include infinite degeneration and instability lines.

Relaxation behavior varies significantly across phases.

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.