Damage Spreading in the Ising Model

TL;DR

This paper investigates damage spreading phenomena in the ferromagnetic Ising model, demonstrating a temperature-dependent transition in damage behavior and revealing that these transitions may not always follow the directed percolation universality class.

Contribution

It introduces the occurrence of damage spreading transitions in an Ising chain with thermal contact and challenges the universality class assumption for these transitions.

Findings

Damage heals at low temperature, spreads at high temperature.

Transitions occur under various dynamic rules, including Glauber and Metropolis.

Not all damage spreading transitions belong to the directed percolation class.

Abstract

We present two new results regarding damage spreading in ferromagnetic Ising models. First, we show that a damage spreading transition can occur in an Ising chain that evolves in contact with a thermal reservoir. Damage heals at low temperature and spreads for high T. The dynamic rules for the system's evolution for which such a transition is observed are as legitimate as the conventional rules (Glauber, Metropolis, heat bath). Our second result is that such transitions are not always in the directed percolation universality class.