Damage spreading in random field systems

TL;DR

This paper studies how quenched random fields affect damage spreading in kinetic Ising models, revealing a complex interplay of mechanisms that influence the transition behavior.

Contribution

It introduces a generalized master equation and effective field theory to analyze damage spreading in random field systems, applied specifically to the Glauber Ising model.

Findings

Random fields influence damage spreading via two mechanisms with opposite effects.

The competition between these effects leads to complex damage spreading behavior.

The theory explains how random fields can both suppress and promote damage in spin systems.

Abstract

We investigate how a quenched random field influences the damage spreading transition in kinetic Ising models. To this end we generalize a recent master equation approach and derive an effective field theory for damage spreading in random field systems. This theory is applied to the Glauber Ising model with a bimodal random field distribution. We find that the random field influences the spreading transition by two different mechanisms with opposite effects. First, the random field favors the same particular direction of the spin variable at each site in both systems which reduces the damage. Second, the random field suppresses the magnetization which, in turn, tends to increase the damage. The competition between these two effects leads to a rich behavior.