The Damage Spreading Method in Monte Carlo Simulations: A brief overview and applications to confined magnetic materials

In this paper we first give a brief overview of Monte Carlo simulation results obtained by applying the Damage Spreading method. We analyse the transition between a state where the damage becomes healed (the frozen phase) and a regime where the damage spreads arriving at a finite (stationary) value (the damaged phase), when a control parameter is finely tuned. These kinds of transitions are actually true irreversible phase transitions themselves, and the issue of their universality class is also discussed. Subsequently, the attention is focused on the propagation of damage in magnetic systems placed in confined geometries, such as the Abraham's Model, the standard Ising magnet (Glauber dynamics) and the corner geometry. The influence of interfaces between magnetic domains of different orientation on the spreading of the perturbation is also discussed, showing that the presence of interfaces enhances the propagation of the damage. Furthermore, the critical transition between propagation and nonpropagation of the damage is discussed. In all cases, the determined critical exponents suggest that the DS transition does not belong to the universality class of Directed Percolation, unlike many other systems exhibiting irreversible phase transitions. This result reflects the dramatic influence of interfaces on the propagation of perturbations in magnetic systems.